2018国考行测备考:你必须get的几何问题备考技巧
孔子·《论语·卫灵公》有云:“工欲善其事,必先利其器。”这就话就是说工匠想要把工作做好,一定要先使工具锋利;也就是比喻要做好一件事,准备工作非常重要。国考的重要性自不必细说,小伙伴们一定要早早着手准备。可自己已经开始备考的小伙伴们说了:“知识点太多了,本宝宝仿佛受到10000点伤害啊!”亲,想知道你为什么会受伤,血槽已空吗?因为你和国考知识点之间差了一个华图教育啊!小伙伴们还记得《择天记》中陈长生带领国教学院在青藤宴上闯关时说过的一句话吗?他说,三千道藏有云:“等长,面积最大者,其为圆。”电视剧播出时,我感叹陈长生之牛气,因为他说的话就是国考几何问题的一个考点啊!
在备考行测数量关系的过程中,很多考友在看到几何问题时,都吐槽说:“几何问题太难了,我只能选择放弃啦。”我个人觉得这话说得欠考虑,因为几何问题在国考行测数量关系中是必考题型,而且顺着华图知识树梳理几何问题,你就会发现几何问题真的没有那么让你“扎心了老铁”。先看看几何问题在历年国考中的出题频率和简要考点。
2010-2017年国考几何问题题目数和简要考点
题目数(道) 简要考点 2017年 3 几何计算(相似三角形),几何构造(最大截面),几何构造(空间几何) 2016年 1 几何构造(面积排布构造) 2015年 2 几何构造(勾股定理),几何计算(表面积计算) 2014年 1 几何特性(立方体特性) 2013年 2 几何特性(相似三角形),几何构造(空间立方体构造) 2012年 3 几何构造(正六边形),几何特性(三角形特性),几何计算(体积计算) 2011年 1 几何计算(构造最大截面) 2010年 1 几何特性(三角形特性)
历年国考数量关系考题共有15道考题,不是每种题型都有机会在考题中出现的。通过华图孟老师的梳理,从上表中可以看出几何问题国考每年必考!小伙伴们禁不住感叹:“厉害了,我的几何问题!就是我们熟知的工程问题、行程问题也没到每年必考的境界呀。”现在知道几何问题的重要性了吧,这个考试的制高点我们应该尽力拿下。
其实国考几何问题考察的是几何基本定理和性质,不是什么高深的难以理解和掌握的知识。华图孟老师在这里就给大家介绍一下国考行测备考必须掌握的几何问题备考技巧。先说说我们以前学过的基本几何定理(或公理):
一、两点之间线段最短
解释一下就是,如果有A、B两点,那么这两点之间的最短距离是线段AB(同一直线上的两个点),而不是折线AB,或者弧线AB,如下图所示:
http://www.huatu.com/2017/0708/data:image/png;base64,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
国考几何问题曾出现此定理相关考点:
【例1】(2012-国家-79)草地上插了若干根旗杆,已知旗杆的高度在1至5米之间,且任意两根旗杆的距离都不超过它们高度差的10倍。如果用一根绳子将所有旗杆都围进去,在不知旗杆数量和位置的情况下,最少需要准备多少米长的绳子( )
A.40 B.100
C.60 D.80
【分析】伙伴们,这类试题怎么想比较关键,结合题目中的几何模型应用相关定理是快速解题的秘诀啊。根据题中要求,要想围进所有的旗杆,同时保证所用绳子最短,就是我们应该设定旗杆排布的最理想状态。因为“两点之间线段最短”,我们把相距最远的两个旗杆看成两个点,这两个点之间最短的距离就是它们之间连线所成的线段了,接下来假设其他的旗杆都排列在该线段上,那么围近所有的旗杆就需要两条最短的线段了,也就是要准备的最少的绳子。我头脑中的旗杆排是这样的(两端的绳子一共是旗杆的外周长,计算时忽略不计):
http://www.huatu.com/2017/0708/data:image/png;base64,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
那么根据题意,最远的距离是10×(5-1)=40米,两条最短的距离就是40×2=80米,也就是应该选D选项。想明白了,本题就很简单了,当然这个“想明白的过程”需要我们学习和沉淀啊。
由这一定理也以得到三角形边长关系的相关定理,也就是我要介绍的下一个定理。
二、三角形两边之和大于第三边
给小伙伴们解释一下就是,
http://www.huatu.com/2017/0708/data:image/png;base64,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
。其实这条定理是第一条定理的特殊情况,三角形的第三边AC可以看成是两点间的线段,AB与BC的和看成A、C两点间的折线,两点间的折线一定大于两点间的线段。这条定理也可以理解成:如果三条线段其中的任意两条的和不能大于第三条的话,这三条线段就不能组成三角形。
这个考点曾经在国考中这样考察:
【例2】(2010-国家-53)科考队员在冰面上钻孔获取样本,测量不同孔心之间的距离,获得的部分数据分别为1米、3米、6米、12米、24米、48米。问科考队员至少钻了多少个孔( )
A.4 B.5
C.6 D.7
【分析】根据题意,如果使钻孔个数尽量少,那么就应该满足题目中出现的这些孔间距离的同时尽量让这些长度能共用同一孔,6条线段如果可以组成下图,那就可以选最少的4个孔了。
http://www.huatu.com/2017/0708/data:image/png;base64,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
问题是这6条线段能不能组成如上图那样的封闭图形呢?答案是不能。因为我们可以看出要想组成封闭图形首先必须能构成三角形,而1米、3米、6米、12米、24米、48米这6个数字中任意选三个,它们都不能完全满足任意两数之和大于第三个数,所以它们不能构成三角形,就不能构成封闭图形了。要想使孔数尽量少,也要尽量应用公共孔,如下图或直线排布,或者散射状排布,无论哪种都需要7个孔才行,选择D选项。
http://www.huatu.com/2017/0708/data:image/png;base64,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
三、勾股定理:直角三角形两条直角边的平方和等于斜边的平方
用直观的公式说明就是如图:直角三角形ABC,的三条边分别a、b、c,其中a、b是两条直角边,c是斜边,那么就有
http://www.huatu.com/2017/0708/data:image/png;base64,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
。
http://www.huatu.com/2017/0708/data:image/png;base64,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
这几个定理有时会联合考察,比如下面的题目:
【例3】(2010-福建-103)一只蚂蚁从下图的正方体A顶点沿正方体A顶点沿正方体的表面爬到正方体C顶点。设正方体边长为a,问该蚂蚁爬过的最短路程为( )
http://www.huatu.com/2017/0708/data:image/png;base64,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
A.
http://www.huatu.com/2017/0708/data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACgAAAAbCAIAAACBclo5AAAA2ElEQVRIie3V0RHDIAgAUOdiIOZhGpZxmOajsSIo0bTa9k6+aprjHYImPL4UYcOt99yYC9/I/rfwx9UN98CRIM0y8jqYESiev0IIaTEFFuVGolxkJHin6CG4CMZ6wYypEZGgvSk3YcZqtYy59UwAziCMw3m6VDFSra2H4OZBOvmc1zAXM5DzVm987wQXFKPeAfukBr8AZbtXh2i06bk7WAKWUi8cCVJqva2mEdewsgu4qEKw6h/GAETPLWBqFe3Bptx0RCsjrW7StOwZLmvP+Db8KrwgNrwsDoQkY1IqKaUVAAAAAElFTkSuQmCCAA==
B.
http://www.huatu.com/2017/0708/data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACMAAAAaCAIAAACyznJrAAAA0UlEQVRIie2U3RHEIAiEqYuCqIdqaIZizMOZiMA5JmNu7s+nxHH2YzcbobxqwU+SYLgWk+blPoG0CvMnlVKEWuuQ9TaSMpp+k5wCDUnR0Fkfl0iHoee0PVsSZQwHZ0l9cjE6obYrjBjPTJNUu7k7HYvJ3sekUb+FbIpBVxkT11DMHTpL6toh5D9J3KmC0J6M+ixJyM2ftWH3dIlU1X1StTnJz+YTsxb7QduYyngodQ6EAJkfJoWdrZwUDNlryEVj+k/SXtNGRNjCi/UNSPetbyRtj39Z0ls6CSUAAAAASUVORK5CYIIA
C.
http://www.huatu.com/2017/0708/data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEYAAAAgCAIAAAAg4ZmUAAABb0lEQVRYhe2XW7bDIAhFGRcDYjyOxsk4GO/HbRQQrdpoVrLCV1ubw9lEfEB8XMDVBs6PF+kO8SLdIa5EgmbMy55ocTj3D75bsitEe3M/DGkRTzSQPKELi5KJxB1IwSH5cWUlAUnDEwBMKPYmZkjB4bEoqITBIYyWWOp+BHOKHUh5XphVFHXuUj4+eFLlCA6XIbFXFJzLOeycg1BQfaoHabbxao1U1PXL77Z4jNGestuRPFXz2S119Ac6R5DHIY1Zc3gXkqdjeajoeVJDwWH6xZN4EMwH0kNbJ96n6pakMiMNq8FhpFzQMqwClAe21o5U2zmEGW1XfV/4lhKMompuspWG4mb0X7T7Hb00iGRJMtuK4H+2cp+bVjxOJZB4m9cXa+6Pz01PgIgA5Nn2Zu9LomEarseRilckUtUqKFDl8alcU+qnh7Nj/m43d3qIcTnUNNKor+Ikvudq0R0Tdb7svtQTJ9yXnhEv0h3iRbpD/AEnqxnWnm98hwAAAABJRU5ErkJgggA=
D.
http://www.huatu.com/2017/0708/data:image/png;base64,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
【分析】要想使AC之间的路程最短,我们就应该想到“两点之间线段最短”,题中要求蚂蚁药沿正方体的表面爬,我们就要把A、C两点间的线段放在正方体表面积构成的平面上,也就是如下图,把正方体的一个侧面展开,然后连接AC,根据勾股定理求AC间的距离,就是
http://www.huatu.com/2017/0708/data:image/png;base64,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
,本题应该选择B选项。本题关键点是如何把AC放置在题干要求的统一平面上。
http://www.huatu.com/2017/0708/data:image/png;base64,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
如果知道考点还是比较简单的,对吧,亲们。我们再来看看2017年各省公务员考试的新题目:
【例4】(2017-吉林-65)悟空与二郎神在离地面1米的空中决斗,两人相距2米,悟空想用分身直接偷袭二郎神,为了不引起对方的警觉,分身必须在地面反弹一次再进行攻击,则分身到达二郎神的位置所走的最短距离为( )
A.
http://www.huatu.com/2017/0708/data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADgAAAAlCAIAAACYrL0MAAABEklEQVRYhe2V2xECIQxFqYuCqIdq0gzF4I+DEUIekHFd5X447q6ce/YVQ71JwtUC2hxR7xxR7xxR7xxR7/yTaJCyX1G9RPchcosDYltUQ/hEh7iK33zuXKgRodaFXy2K1zLSr/3oe8mxvakxF1vZAmEUZU67HSg5NjQktStCLxJ4v0G0AGBoyVHR81agJohzl5y+s1OBZBVdImBv4Wf07pKj5SHbJOBPmygk7cWYHTIRVkXxW7FkaSWY3nqhZHyM5lCV5mx2auZorbVCCgloaOc6I5IExlLcJES7jpJTd2GwK4kzERgz4gbijj7DDeRFNQQyhoFPdEjjWrZU/zUZRE3RzGf3/LToJTmi3jmi3rmN6ANUp2DMOELFmAAAAABJRU5ErkJgggA=
B.
http://www.huatu.com/2017/0708/data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACoAAAAjCAIAAABtrg/EAAAA3klEQVRYhe2UWxaEIAiGWZcLYj2shs2wmOnFsrwQ6Ix1zshDJ63fD+QCn0cNFn7hF37hX4gH1WbgRxgP4xX5/bkd7EyiLH+Czxnz8Weh5ooLLxT2ekf248tIPHjGQBLfAGBfOE4oP5mVQpQCFgqtC9CHRDYt7PiLMVqD16dTD57RkvokPz/H8Kn2TMEP4ZslE524uQFf5ZcZ0jqeUee3er3e98f9KL+W/Ba+c+g68EKhlv5qkVd3YsCK/iITCqneGvCGOcZO8ivXMKaZYUc78YcHauK/Zu/Dz7SF/1/8Bi72vAml9GgLAAAAAElFTkSuQmCCAA==
C.
http://www.huatu.com/2017/0708/data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADEAAAAfCAIAAADBWLINAAAA40lEQVRYhe3VwQ2DMAwF0MyVgTyPp/EyHoYekGjqOsmPKYRK+QdEK2yeLDBpe17SbICTZcKyTFiWCcsyYRkzpV7mmM7eD+hwucmUtH8Om8JDKgufYiprG775pka3mEk5H69aZo3gWteMt1POh0OoyeruDneDoKZ3pYqUAuUMzwpcY+MmGyHMtHcoj5eZlDM2pvtMQgNDck+CptaQAFFtJ6H7yX0MK8WQKPJtUe8Kw3IrhRJJR+O8594/Foq0+25kQMoEbs5TO7NkmUb7ovwIvMx/Y+qDRr8vYdNWed5vyL+ZZuUFAeY8/DAxK+UAAAAASUVORK5CYIIA
D.
http://www.huatu.com/2017/0708/data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADgAAAAiCAIAAACFqY20AAABLUlEQVRYhe2VWxLDIAhFsy4X5HpYjZthMelHE4MPECrTNFPvR2di5XIkQrb9IdruBtBqgXprgXprgXprgXprgXrLE3QTNWvugnh4TdNI5m5Gc5TD8NtAq/3y435vRWnIT4PSKAH6WGxWEELu1ABopiTxMdlBuQNXqwghw6WoZr3cUzwDUjSc1NpMmBI1Rgi6XGcaBLiKiBC4osoTtzt65XOkaAOtg5UF1XwURFCEoMjFUSqu6BVOf/vbBAtlSWr3q5sM93sClPaVCTSHKxr/464fYPavOVeGFGVSbnYq5+iRok2Q387QlJJyoOZPaHuRKkqEWO2grBIo04vdBu+uFBWp/n5P+UJNLnoBigTF3NWNDB603jCgZFq3D1oY6CHtoCYNR7Sv/gD0y3oM6Au8LHC92OZQQwAAAABJRU5ErkJgggA=
【分析】看到题目就有一种莫名的喜感有木有啊,还慢慢开始明白了“牛人都得会几何”,因为就连打架也可以用几何知识做技术支持呢!本题中如果我们把悟空分身和二郎神都看成点的话,题目所求就变成求两个点之间的最短距离了,小伙伴们一定想到了“两点之间线段最短”,那么我们就要分析一下这个最短的路径是哪条了。先画图分析下:
http://www.huatu.com/2017/0708/data:image/png;base64,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
题中有要求,分身要在地面反弹,就是这个最短的线段要与地面有交点。同时大家要注意悟空的分身一定是从悟空本身发出的,我们就要找出由悟空本身发出,经地面到达二郎神位置的最短的路径。如图,路径可以是从悟空发出,经地面上的P点后到达二郎神。
http://www.huatu.com/2017/0708/data:image/png;base64,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
但这条路径是最短的吗?小伙伴们表示,似乎不是很好判定啊。我们的定理是“两点之间线段最短”,我们应该想办法把经地面连接悟空和二郎神的路径放在一条线段上,那条线段就是最短的了。小伙伴们有没有想起对称点呢,就是我们把悟空分身的出发点先转换一下位置,这个位置是以地面为对称轴的悟空的对称点,这时我们链接悟空的对称点和二郎神,这条线段就是这两点间的最短距离了,这条线段与地面的交点是O,由对称性可知,悟空到O点的距离等于悟空对称点到O的距离,那么也就是最短路经是经悟空到地面上的O点,再到二郎神,这条路经就是由悟空、悟空对称点、二郎神三点组成三角形的斜边,长度是000000000000米,本题应该选择A选项。本题中悟空的对称点和二郎神之间的连线就是最短的线段,而悟空对称点到P再到二郎神间的折线就不是最短的。
http://www.huatu.com/2017/0708/data:image/png;base64,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
用语言描述过程比较复杂,如果我们get到了该知识点,解题会非常快的。再比如,2017年422联考的题目:
【例5】(2017-湖南、湖北、浙江、重庆联考-47)如下图所示,某条河流一侧有A、B两家工厂,与河岸的距离分别为4km和5km,且A与B的直线距离为11km。为了处理这两家工厂的污水,需要在距离河岸1km处建造一个污水处理厂,分别铺设排污管道连接A、B两家工厂。假定河岸是一条直线,则排污管道总长最短是( )
http://www.huatu.com/2017/0708/data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAXEAAAD0CAIAAADi74EsAAAgAElEQVR4nO3deUCTV743cKcdO7d3OnM77bR3+jpOrW2nOmNr93Za3Fs33EClWhWL7IjsiqwhhIQl7HsEWWVfBNkFEvZ9XyQsgSyQsCRAdrLy/vFYLgXUKCEJ5Hz+0hDy/KLhy/Oc83vO2TQPAAAgP5uUXQAAABsKyBQAAOQJZAoAAPIEMgVYFZFIxGazp6enZXy+RCIRCARrWhKgXCBTgFUhkUiRkZE2NjYyPn96erqlpWVNSwKUC2QKsCpCobC7uxuJRJ4/f57D4bi7u2toaOx4sn/+85+ffvppVFQUk8lUdu3AmgCZAqwWl8t9+PDhV199xWKxuru7Hz58mLcSJBL5yy+/2NvbFxQU1NTU8Hg8ZRcOrAmQKYAcTE5OJiUl0Wi0kZERNpu94nPKy8u9vb3T0tLEYvHs7KxYLFZwkYBigEwBXlxvb29qampxcfH8/LxQKGxsbMTj8Q0NDUQiEXoCh8NJTEwkk8lCoXAhU5RaMrDmQKYAL660tPTnn3++evXq0NAQn8/PzMxkMBhRUVGBgYH5+fn5+fmJiYl///vfs7OzZ2ZmQKaoCZApwKqUl5c7OTmFh4ezWKyMjAwoUw4cOLB9+/aPPvrogw8+eOWVVyIiIsbHx0GmqAmQKcCqTE9PEwgEAoHQ19eXkZExPT0dFRUVGRk5MDAwPz9PpVJ37twJ/RlkipoAmQKsikQiEYlEo6OjkZGRXV1dfD4fZIqaA5kCyMHIyIizs/P09LREIgGZouZApgCrxWQya2trPT09+Xz+/Pw8yBQ1BzIFeHGdnZ0xMTGOjo62traZmZnQjTxRUVHGxsY2NjZIJPL27dtvvfVWX1/fPMgUtQEyBXhxOBzOwcHhm2++2b1798DAANTGlpCQYGBgoLMImUyeB5miNkCmAKuVmJj4zTffLPy1oqKiq6tr+dNApqgJkCnAqkgkkri4uMWZ8iQgU9QEyBRgVSgUCgwGA5kCLACZAqwKiURydnZ+eqbo6Oh8+eWXH3300dmzZx8+fKiw2gClAJkCrAqHw+nq6np6UhQWFqakpHh6et69e3diYkJhtQFKATIFUBAajUalUpVdBbDmQKYAACBPIFMAAJAnkCkAAMgTyBQAAOQJZAoAAPIEMgUAAHkCmQIAgDyBTAEAQJ7knyl8Pp9CodSvpK6urra2FovFVlVV1dXVQQ82NDS0tbXh8fh+mVGp1KmpKbpsmEymUCiU+9sEAGBF8s+UycnJzMzMsyvR1tY+ceLE9u3b//Of/5w8eRJ6UEdHx8DAwMnJCSazmJiYtLS0DNkUFRU1Nzf3yWxwcJBIJJJkQyaToYCTEZ1OZ7PZHA6HK5u5uTmpVCr3/yMAWDtrcu0zMzNTsZLy8vLU1NS//e1vxsbGGRkZ0INlZWUpKSlIJBIuMx0dncOHDx+Szeeff/7WW2/9Xmbbtm3bs2fPQdmcOHHCwMBA9jT08fEpKCgoLS0tkwEOh+vu7uZwOMLnIXoe4ucheU4gDdXTmmSKRCLhr4TNZuPx+HfffReJRBIIhIXHORzO7POYnJwclxmVSqVQKDKed5BIpObm5ry8vBzZpKamhoaGyp4pt27dOnfu3OnTp0/J4MSJExoaGtu3b98qs0OHDkGnfrIwMDBwdXX1l1lSUlJlZWWdbNra2kZHR9fi0wWoOIWO0QqFwpGRkW3btnl7e6vsB47P58/Ozk7Lhk6nj42NDctscHCwo6OjTTatra0NDQ04HA4rs7S0tLi4uBjZhIeHe3p6yh6INjY2165d+0U2ly5dOn369H6ZHTlyxMzMzNLS0koGNjY2cDj8zp07sTLDYrEtLS3tshkYGJidnVX2J3G9ApmyoUxPT0O3/8piZGSkp6enVWbV1dVFRUUFssnNzU1JSYmW2Z07dwICAvz9/f1k4+Xl5ebm9lxniNYyu3HjhrGx8TWZWVtbo1Aob9kEBATcvXtXxhPhnJycgoKCrq4uGUcD8Xj82NgYtNi4sig0U0QiEZlM/u677yIiImg0miIPDaia0dFRJpMpEomgvwqFQhKJRJDN0NBQZ2cnDoeTZVgKkpycHB0dHSWb4OBgBALhIDNHR0fn5+Hi4iJ7GsJgMPengsPhLi4uLi4u0F8RCATyeURGRiYkJCQmJqakpMhlxSyFZopYLJ6ZmQkMDKypqWEymYo8NKBqAgICqqurN8bHYHp6Go/H98imvb0dh8OlyywpKQmFQsHhcLcnsLGxOXz48L59+xb+evnyZRnH1HR0dPT19c3MzK5fv25tbR0aGrr6fw3Q8wYox/bt2318fMAl8Orh8XhDQ8OzZ8++2LePjIy0tbW1tLR0dnZSKJTV1wMyBVAOkCnysspMkTuQKYBygEyRF7XOFIlEwmKxkpOTOzo6OByOIg8NqBqQKfKi1pkiEolGR0cPHz589+7d8fFxRR4aUDVHjhwBHwO5GB4ednV1tbS0VHYhj4H+FEA57t+/39PTw+VylV3IusdkMuvr6ysrK5VdyGMgUwAAkCeQKQAAyJOiM4VIJO7atSsgIGBsbEyRhwZUDYvFmpubk0gkyi5k3ROJRNDKGMou5DFF99FOT0/7+vpWVVVtjAZK4IWFhITU1tayWCxlF7LukclkaKkgZRfymEIzRSqVisViBoPB5XLFYrEiDw2omi+//DIkJATsdrp6jY2N165d09PTU3Yhj4GeN0A5QH+KvNTU1Jw7d05N+1MAYAHIFHlR60yRSCQcDqeoqKi/v5/H4yny0ICqAZkiL2qdKVAf7ZEjR2JiYkADpZo7ePBgVFQU+BisXmtr640bN8zNzZVdyGOgPwVQjvj4+NbWVjabrexC1j0qlVpYWFhYWKjsQh4DmQIAgDyBTAEAQJ5ApgAAIE+K7qNlMBgoFAqHw4G9DtQcBoNpbGwEfbSrNzo6WlRUJJflqeVC0X200PLoMzMzCwumA+pp3759GAwGbJ+wei0tLfb29s7Ozsou5DHQ8wYoB+hPkZeamhp9fX1TU1NlF/IYyBRAOUCmyItaZwp0D+Hs7Cyfzwc3uas5kCnyotaZIhKJSCTS7t27g4KCwPopag5kiryodaao51xyY2Oj+rxZ2SUlJbW3t4PtE1aPRqPhcLiqqiplF/IYyJSl0tPTYTBYV1fX059WUlJSXl4uy+0q0dHRRkZGqampMhbQ2Njo4+OzfJfJwsJCa2vr8vJyGV+HxWI1NjYun1/jcDhxcXHT09NLHszNzX1mpzydTs/JydHV1W1paVnlXaB0Op3D4YBldFZPKBQymUzVmZUHmbJUcXGxkZGRlZUVmUyWSCStra1BQUGOy3h4eCCRyKKiome+oK+v75UrV2TPFAwGc+LECQ8PjyWPR0ZGHjhwoKKi4pmvUF5eHhMT09DQcPPmzeWV29jYfPnllwUFBYtbhBgMxu3bt5c/eQlXV1cUCoVEIoODg8FySsCKQKYsxeFwEhISzpw5Mzg4CJ1Vuri46C2Tnp6ekpIiy1mDr6+vl5dXc3Pz4gfpdDqfz1/+ZB6P5+joeObMGRwOt+RLsbGxFy9eJJPJSx6fnZ1taGi4uwgMBnN2dg4PDz969OjZs2d1dXW1tbW//fbbvXv36unpXbhw4fXXX09NTV18qjI1NWVqavrjjz9euHBh+ZtdcOvWrfz8fKFQmJ6ePjk5KeM/KaBWFD1GOzY2duzYMRVf66C3tzclJWVubg6Hw63+lNLX19fGxqakpAT6q0QimZycTEpKqqyspNPpS55MoVCuX79uZGREp9MlEgmPx2toaICe9qRMIZPJISEhe/fu3bt371tvvfXhhx9iMJiRkZGQkJCLFy/29PTMzc319fWFhoYmJCTMz8/TaLR//etf/f39i18EypSYmBiFnX00NDSQyeS5uTnFHG4Dm5qawuPxIyMjyi7kMUXPJfP5/NbW1tHRUYFAoMhDy4LJZM7OzkKfcmg57pycnJmZmSc9n8vl0un0FW8ygOKAQqGIxWJfX9+zZ8/GxMSIxWKJRMJkMmNiYr7++uuLFy9isdgl39je3u7i4uLp6Ukmk4eHh2tqarZu3ZqRkSEQCGJjY8+dO9fd3f2Ut3D+/PmIiAgGgzE/Pz88PGxpaYnFYgcHB7FYLAKBCAwMJJPJra2tH374IR6PX/yNis8UMO8jL7m5uXp6eq6ursou5DFFZ4pUKpVIJNAfFHloWfj6+rq5udXW1s7Pz09NTWVlZfX39z/lF2lmZqauru6K/5fQcnb/8z//MzY2BmVKYGDgxMQEi8UqKSn57LPPWlpahELh8iadO3fumJqa7t+/f/OvNm3apK+v39raGhsb+8knnxgZGT3lLSzJFD09vT/+8Y/Q67z88ssvv/wy9Off/e53S7IJZMr6pdaZouLodDoKhTI1Nb1///7U1FRSUlJERMSePXt2PIGZmdm9e/dycnIqKiqkUmlQUND+/fuhL3300Ufbt2/fvn17QEDAzZs3b9265ePjExcXl5CQoK+v39XVteJgyvz8vLW1NQKBaG9vf/ToUWNjo52d3eXLlysrK3k8Xmxs7I8//ohCoXbu3Hnw4MG2trbl374kUywsLPLz8zs6OvLz852dnb28vB49elRVVfX+++8r8TxFLBZPTk5u27bN3Nz86addgCxApqi0iooKBAIRFxdHpVIjIyPxePzDhw/z8vIcHR21tbVv3ryZt0h7e/v4+Pjk5OT4+LhUKsXj8aWlpdCXgoKCNDU1L1682NbW5uHh4e3t7eLiYmhoiEajW1pannT/5NDQ0KVLlzw9PaHhz8nJycuXL6PRaCKROD8/D137NDQ05ObmXr169eTJk2lpaSwWa3JyMiMjQ1NTU1NT85133vn4448PHz5848aNyMjIS5cuPdd4SnZ29tTU1Nr987LZ7OrqanNz8x9++OHVV1/9xz/+ceDAAVdX15aWlrU76Ian1pkiFovpdLqbm1tZWdlTximUaHp6urOzs7q6ura2Njc3VygUQo9jMBgzM7PlczFPUlVVpaWlFRsby+FwfH19AwICgoODobmYp3xXYmKin59fTEwMdA5CJpPfe++9srIyqG1kYYxWIpHU1taePn3a3d19aGiIxWI1NzcHBgYGBgZ++umnOjo6KBQKg8GEhoYePXpUV1f3+vXrV65c2b9//+HDhy0sLAwMDN54443e3t7Fhx4fH9fR0cnLy1vStyJHHA7nwYMHJ0+e/Otf/7rpVy+99NK7775raGioOi1b645aZ8q6mEuen59vb28PCQkZGRmBxjuGhoZMTU2/+eab27dvB/1WQUHB8rkbNpudmZl55syZ4eFhkUgEZUpJSUlycrKTkxOTyVw+jAKN3cLh8MrKyuzs7JycnLm5uZaWlm3btg0NDUHPWTLvk5ubW1hYSKFQFr/OwrUPi8UqKys7evTolStXzMzMLl++vG/fvh9//PHGjRsmJiYaGhoEAmHxN1Kp1CNHjjx8+HDt9oesr6+/dOnSyy+/vGmZt99+W19fn0ajgRa4F9DU1BQaGpqSkqLsQh4DmbKUQCAoLi6+ffv2wiN1dXX29vbHf+vbb7/95z//aW5uDl2YLNbd3Y1Goxd+b0CZ0tnZWVFRcfXq1cLCwuVzXgKBoK6u7u7duwQCoaioKCkpqbe3NzY2FvpJg57zpLnkxRaPp1AoFA8PDyKRKBQKF1/78Hi87OzsJdNVY2Nje/bsaWtrW6PJXZFI5OXl9f/+3/9bHiiQrVu3PnjwAOzQ8gKYTCaFQlGd5gyQKf+HTqcPDQ01NDTExcUFBwc//cnl5eUeHh7LN6kVCATJycmmpqaVlZXQIwuZMjY2FhMTo6WlNTQ0tHBVBeFwOOHh4dBYxqNHj5KTkxEIhIGBQV5e3kK//HNlCofDWfwhW5wpIpGIQCAsyTUSifT++++vXY/D9PS0sbHxkwJl06ZNb7zxhp2dnWpeEQPPBWTK//H19d25c+dLL720Z8+e0tLSpz85IyPD29t7+dP6+/t9fHwQCMTil4UyBfrqiRMnDAwMhoaGFl8BQecpCzfUpaSkbNmy5b333lt8LSBjpoSFhU1MTJSWllpaWgp/1d3dHRQUFBsbKxQKKRTKJ5980tfXtzCdL5VKiUTihx9+uHaZ0tXVdf78+adkymuvvXbq1Kk1HSEGFANkyv9hMpljY2OWlpaHDx9ecaZ2scjISDQa3dTUtORxT09PBweHwcHBhUcWZ4pQKBwYGNiyZYu+vn5HR8fCc6RS6dzc3ELK4HC4q1evWllZLc6d4ODgQ4cOPTNTtm7dumXLFm1t7dDQ0K2/euedd/7yl7+8+eabW7du3b17d2Vlpaen58Iw7ezsbFlZmZ6e3tqdP5NIJF1d3adkyuuvv25qarp2I8SAwih6b1Mej1dXV0cikVS2KdvV1fXUqVPP/I1tZWWFRqOXDJFmZWWFhYXV1NQsvrJYnCnz8/N8Ph+DwXzxxRdffPFFWFjY8rP99vZ2f39/S0vL27dvHzhwYCFE6urq4uLilje2DAwMuLm57d+/f//+/aGhocXFxVgstr29fWxsDPuruLg4CwsLBwcHLBZbU1PD4XAIBMLCVRWZTL5z505mZuba7eA1MzNz/fr1FQdoIX/7299CQ0NV5+badaS2ttbb2zs2NlbZhTwG+lN+g0ajmZuba2lpPf00qrOzU19fPz4+fuEnXCqVtre3x8TEVFdXL/nBWJIpEolkYmIiKipq9+7dX3/9NTTGsaCioiI0NDQ+Pr6hoaGhocHLy8vExOTatWvXrl0zMjKKiIhYXgydTi8sLHRwcIiMjBweHl4yUgNZPJ4C6erqWjgp6O/v9/DwoNFocl94HFrVvLa2FoVCnTlz5t13310xUP77v//7wIEDg4ODKxYPPJ1azyWrPjwe/8svvyzPFB6PV1tbi/yVrq7uzZs3GxoaFp4glUojIyPLy8uhqWUmk1lfXw89+dixY87OzguZApmdnY2Pj3d3dy8qKoK2kfbx8UEikSgUKjk5eWBgYP7XrUvQaLSDg4Oent6ePXsOHDiAXCQgIKCurm5+fl4gEJBIpIXBl+rqauRvWVlZnTx58vz58wuPXL16FYPBDA8PMxiMurq6zMxMud8tweVyOzs7w8PDEQgEHA4PCwtzdnb+7LPPlgTKSy+99NFHH3l5ecn36OpDrTMFWo9WlRfjGRsbCw8P9/X1haZjF7BYrOzsbB0dnXPnzh08ePDs2bO5ubmLnyOVSlNTUxeSiE6n5+bmnj9//ocffvjiiy/QaDSJRHrSQQUCwcDAwOXLl3V0dOLj41c8RSIQCGFhYTq/ZWBgkJOTs/zJmZmZOjJAoVBdXV1dXV1paWlTU1NyzBQ2m93X15eTk+Pj42NsbBweHj4wMCAUColEYlhY2P79+//9739v2bJl27Ztu3btOnjwoL6+fkREhEAgUMG7wFSfWmeKRCJhsVjretFAgUDQ0dHxpLt1lpBIJD09PRkZGYuHbFVNa2ur7OtFPZNAIIDGcVAo1OXLl93c3Mhk8uIrGhaL1dTUhMFgbG1tYTBYdHR0bW1tYWHhtWvXWltbVfBuddWn1pmi4vM+wAuDzkC5XG5/fz8MBtPS0nJxcenr65Px2+l0enZ29vHjx8lksmqewKqywsLC69eve3p6KruQx0CmAHIA/c+6ublpaGjAYLC2tjYulyt7OkgkEhqN5uXl5eTkNDw8vKalbjwCgYDNZnO5XGUX8hjIFGBVRCLRo0ePvL29z507h0Qiq6qqRkdHZbw2XPI6FArF3Nw8ISEBfDbWNZApwIt79OhRWFiYtbW1l5dXdnZ2b2/vC6TJAolEUl9ff+vWraysLND8tn4pej1aCoWyZ8+eyMhIsPn2+iWRSIaGhhITE5FIpLu7e3R0dGtrK5/PX+WsjVQqFYlEaWlpCARixTstgRVBa+is3Q3lz0vR8z6zs7ORkZENDQ2gY3I9mpubI5PJhYWFgYGBdnZ2aDS6rq5Ovlfys7OzGAzG09Ozvr5eji+7gTU3N6elpUFrnqoC0PMGyEQkEk1MTDQ0NNy5c8fAwMDW1ra6unqNfjeSSKSQkBA4HP70m5sASExMzC+//LJ8kzllAZkCPA20JjmbzSYQCLGxsZcvX75y5UpVVdVaX5i0t7ej0WgvLy8ulwsa4Z4OZAqwnkilUiaTGRkZefjw4StXrpSWlkLL/a/1zzm0PqaJiUl2drbK3m6qItQ6U6AVEuPj41tbW9fuFlhAXmZmZmJiYqDFvQsKCkgkkiK7n9lsdkVFhba2dnNzM1j/7SnUOlOgeZ8DBw7cuXNHdZa6A5ajUqmpqamGhoaOjo6pqant7e0zMzPLl9FdU1KplE6nQ2V0d3fL/Z7pDeP+/ftOTk7JycnKLuQx0J8C/Mb4+HheXp6np6erq2toaGhVVdX09LSy+uWhnYCQSKSvr6/snf7qZmRkpKmpaWEtdKUDmQLMz/96WVpWVhYWFubq6opCofLy8lRhdVixWNzf3+/s7JyQkACmgdaFZ2fK5ORkY2NjUVHR8nUSnxfIFBUENQ21tbWlpKTY2dlZWVmlpaWNjY0pu67fKCsrc3d3T09PX3F3akClPCNT5ubmUlJSDh069MYbb2hqaq7yYCKRiEQiffbZZ8HBwQrblxd4EqlUyuFwiERiYWGhhYXFoUOH0tPTl29XpCJiY2Pd3d3Ly8vBWnBL8Pl8FoulOsPYz8iUjo6OU6dObd++/fvvv199pojF4pmZmaCgoNraWtVpJVZP0NrARUVFurq6Bw4ciI2NVfE2EIFAEBoaamFhQSAQpFKpilerSK2trVlZWYtXHVSuZ2SKmZmZrq6upaXl6dOnV58pUAMVk8lcvEY8oBRYLFZXV/fy5cuxsbHDw8NsNlvFf0qlUuno6GhkZKSZmRmLxVLxahXp3r17pqamd+7cUXYhjz0xUyQSSW5u7o8//hgWFpaWlqatrb36TAGUDtoF3cTExMzM7O7du01NTRMTE+tlGSShUNjV1eXr6wuDwVZzA/QGsz76U0QiEY1G09TUtLS0bGtrKykpAZmy3rFYrNraWi8vLzs7u4CAgMLCwtHR0XU3NsHhcBoaGmxtbdPS0lRhWkoVrI9MmZ6eDgkJ2bt374MHD1gslrwyRSKR8Pn8xsZGMpkMGq4VhsvlNjc3R0dHw+FwDw+PhIQECoWy7tJkwezsbFFRkamp6fJtT9TTOsgUaN+JTz/91N/fH5pTlFemiMXiiYkJU1PTnJwclZ1f2DCgUdje3t6srCwUCmVnZxcWFgbt8rHecTgcf39/Dw+P1tZW8MspOzvb0dFRpftoSSSSu7v7yy+//ODBg+bm5ubm5tDQ0AMHDmhoaLS0tIyOjr7wPamgP0Vh+Hw+mUyurKxEIBA6OjpoNHoj9aFCW8FaW1uHhYUNDg6q+Xg/Ho/H4XA9PT3KLuSxFTKlt7dXX1//9UVee+21zZs3b968+e233/bw8HjhhiiQKQogEom4XG5HRwcMBvvuu+/c3d2JROJ6GYV9LkQi0cbGJiIiAiw0qVJWyBSRSMRmsxmLZGZmnjhx4vDhwwwGg8vlvvCvBZApCtDR0XHr1q1jx465u7sPDg5C27NtyJlXsVhcVVXl6uoaFRWl7FqA/yPT/T7yGk8BmbJ2oDVi4XC4oaGhj49PVVXV2NiYUCjckGmygM1mZ2VlIRCIvLw8ZdcCPKbQTFkYo71//z4Yo5WXubm5/v7+gIAAMzMzb2/v3Nzc/v5+1enUXms0Gi0pKcnJyamjo0M9B1bweDw0l6rsQh6TKVMIBEJmZubqd8AEc8nyJRAI8Hh8YmKim5ubu7s7BoPp6OhQw8WuBgYGwsLCYDAYjUZTw2VWkpOTPTw8ysvLlV3IY2DtyPUH2kh0eHg4Pz8/ICDA0dERhUI1Nzer7eYVIpGop6fHwcEBg8FMTEyo29kKGo2+cuVKWlqasgt5DGTKOiMSicbHxxsaGiIiIoyNjZ2cnKqrq9dvA5u88Pn8jo6OCxcuFBQUqNs0kFpnCvQLlk6nP9dmugAEmo8jEAjR0dFHjhy5ceNGdXU1uO1lAY/HKykpMTAwqKqqUqsra7XOFOg2osuXL6empk5NTSny0BsAhULBYDAHDhy4dOlSc3Mzm81WwPr16wh013twcLCbm5vq3PivAGqdKUKhkEgk7ty5c6HrH5AFjUaLjo7W09OztLQsLi6GNjlXt1EDGTEYDAQCERAQgMfjlV2LgpSWlkJ7USi7kMfAerSqSywWT09PJyQkmJubOzk5paWldXV1gcUTn6mrq8vT0zMsLGxyclLZtSgCg8GgUqmqczslyBRVJJFIxsfHoT0W4HB4ZGRkdXU1uFqUkVAoxGKxnp6ed+/eVcOpZaUDmaJyqFRqaWlpSEiIq6uri4tLcXExg8FQdlHrDIvFysnJcXJyKi0tVXYtakfRY7RUKlVLSysxMXFiYkKRh14XGAxGe3t7YmLirVu3LCwssrOzWSwWGDd5MdC2ZxYWFkNDQxt7rp1EIg0ODqrORbGi55Ln5uba29upVKraNmgtJ5FIuFwumUzOyckxMjIyMjICm07IxfDwsI+Pj6ur6+jo6Aa+CAoNDXV1dW1paVF2IY+BnjdlgqY/Z2dnsVjs0aNHjx07lpSUBM7g5Gh0dPTEiRPJycmTk5Mbdd7d3t7+0qVLWCxW2YU8BjJFmTgcTnl5ubGx8cmTJzMyMkZGRqClCZRd18YhEAgGBgbOnj1bWFi4Ue+EApkCzM/Pz3O53JKSkps3b5qamkZHR7e2tjIYDJAmcieVSoVCYWFhoY2NTUlJyYa8AlLrTBGLxVNTU/b29kVFRep2U8YCoVCIw+Hc3NycnJyCg4OLiopU5y71DUkqlTKZzOjoaG9v76qqKmWXI39qnSlqPpfMZDKbmppCQkLgcDi0++/w8DA4N1EMIpEYFBQUEBCwkdblhaSmpoaFhfX29iq7kMdApigCm83u6enJzMxEIpGGhobR0XU1PzIAAB/VSURBVNFkMnlDnoersqamJn9///Dw8A3WXzs+Pk6hUDgcjrILeQxkyhqSSqUCgYBMJpeVlbm5uV29ehWNRtNoNNByoiylpaUODg4ZGRlzc3MbdRpI6UCmrAloVQcOh9Pb22tra6upqYlEIoeGhpRdl7qbm5srLCw8f/58b2/vhl+sV1lApqwJPp/f29trb2//1VdfodHo3t5esGSMKpBKpVNTU1lZWcePHx8bGwMnjGtBCX20HR0dG7iPViQSdXR0oFCoixcvotHoxsZGGo2mVksEqTiRSEShUAICApycnEZGRpRdjhyEhIS4uLg0Nzcru5DHQH+KPHV0dPj6+trY2KDR6AcPHgwMDICBWBUkEAiGhobs7OygraOVXc5qqfVc8kYlFAoJBMLdu3cRCAQCgYiLi+vo6ADnJqpMLBZXVlY6Ojrm5OSs99u+1TpTpFKpSCSamJhgs9kbY3CBz+cTCIQHDx74+/tbW1sHBAS0tbWpz946611cXBwKhSotLV3X/2VqnSkSiYTJZMbExEDLqSry0HInFAqpVGp1dXVoaKihoaGlpWVLSwuXy1V2XcBz4HK5wcHBSCSyra1t/Y7XqnWmbIB5H+hOYhaLBe1TdfHiRRMTE7VaUXmDGR0d9ff3d3JyWr+NcCgU6saNG7W1tcou5DGQKc9HIpHMzMyEhITs37/fxMSkpqZGJBKt319xgFQq7erqQqPRLi4uyq7lBYlEIpX6EIJMeQ5UKjU8PPzYsWO3bt0qLS2lUCjr+jocgMzNzVVXV9vb26ekpICR9dUDmSITIpEYHx9vbm4Og8GysrK6urrAqo4byezs7MOHD69evdrY2AgGxVYJZMozjI2NZWRkIJFINzc3DAZTX18Pbdal7LoAOZuamoqNjbW2tu7q6lpfZysTExMq1Vep6PVT6HQ6DAYrLS2dmZlR5KGfl0gkmpqaKiwsDAoKcnZ29vHxKSkpUds1X9SBRCJhMBiOjo5BQUH9/f3r6NdGcnJyXFwclUpVdiGPgZ63paDga25uTkxMtLCwsLa2fvDgAVgjVh2IxeKBgYGbN2/eu3dvHe2TaWBgcPHixZ6eHmUX8hjIlP8jlUpZLBaBQMjKyjIzM9PW1i4oKFCd7d0AxcDhcM7OzmlpaaqzIsnTqXWmSKVSqL8D+oMiD/10UFVcLjcrK+vcuXMnTpxITU3l8/kqVSSgMImJiW5ubkVFReviA6DumcLn81tbW0dHR1XqvmShUFhUVHThwgVDQ8PU1FQikcjhcFQt+ACFmZmZwWAwzs7O3d3dyq7l2dQ6U0Qi0djY2PHjx2NjY1VkhGJ6erqkpMTAwOD69evx8fGtra1TU1Mb414k4IVJJBICgRAZGenk5DQxMaHi47VqnSkqNZc8OzuLw+G8vLzs7e1DQkIePnxIpVI39iaYgOyEQmF7ezsajfbx8YFOWpVd0RNVVVVhsVjVmZRUu0yRSqUcDqe2tjYiIsLNzc3T0zMtLQ2sEQssx+Fw6urqbG1tMzMzwVazslOjTJFKpVwut7OzMzU11d3d3dbWNioqanBwUMFlAOvI7OxsYWGhqalpTU0NmAGUkaIzhUgk/vvf/w4ICFDw/D+XyyUSiVgs1sXFRUtLKzQ0dHh4WJEFAOsUm80ODAx0d3dvbW1VqYmFBXw+n8fjqc4goKL7aMfHx/X19TMzM+l0umIOKhKJOBxOfX29nZ2dhoYGGo2empoCVzqAjKDJSisrq7CwsKGhIRUcWOno6GhtbVWd0yhFzyVLJBI2mz03N6ewn+q2tjYLC4tTp075+fkRCAQejwc1yCjm6MB6B7UUkMnkGzduREZGMplMZVe0lLm5+bVr1x49eqTsQh7bsH20AoEAj8fb29vr6ekFBgbW1dXRaDQwrQO8GKFQWFVV5e7uHhMTo2qfIrWeS1YMHo/X2dmJRqONjIz8/Pzy8vKGhob4fL6y6wLWNyaTmZWVhUQi8/PzlV3Lb6h1pkgkEh6PV1NTQyQS1+KHXCAQ9PT0xMfHu7m5eXh4REVFPXr0CCybBMgLhUK5d+8eHA5vb29Xnctntc4UaIzWwMAgKytLjmO00EaiAwMD9+/f9/X1dXJy8vPz6+jokNfrA8ACPB4fEhLi4eExPj6uIps32drampqa4vF4ZRfy2LrvTxEKhTQarba2Nigo6Nq1a25ubvX19ap2xQtsGGKxuKury8rKKj4+XkUmEFNSUuLj49fT+inT09MUCmVycnL1k/PyzRSRSMRisfB4PAaD2bt3r52dXVtbm+qsdgVsVNAl9sGDB7FYLIvFUp2LINnNzc1RlpHXzgHPzhRTU9PNmzcfOnSovb19lQeTb6YMDw/7+fkdPHhQT08PGjcBk8SAAkAdKzU1NT/99FN1dbWKXAE9l4qKis3LaGpqyuXFn5EpDQ0NFy9e3Lp163fffRcYGLjKg8krUygUSnBw8NWrV+3t7cvKysbGxgQCAUgTQGGg2QYMBgOHw+vr65VdznPD4XCvvfaapaVlbW3to1+RSCS5vPgzMsXX19fY2Bha9Ozo0aOrPJhYLJ6cnLSwsHjw4MELbFIrEoloNFpsbKyJiYmbm1tWVlZvb6/qtA8C6mZ0dNTHxyc0NLS3t1dZNUATqY2Njc81kYrD4f785z8jkcipqSm5l/TETJFKpdPT0+fOnXNyciouLnZ2dv7www/b29tXM/wplUrn5uba2tqgMwvZv1EsFpPJ5LS0NCcnJzgcHhUV1dDQoDo3dwNqq7W11dvb+86dO+Pj40opgE6nOzs7e3t7P9ePg3IyRSKRVFZWfv/99yEhIVNTU/fu3Xv//fcRCITizwtGR0eLi4sDAwNdXV3d3d1LS0vBuQmgIkQiUUlJiaenZ3JyslI6oWg02k8//WRiYvJci5zhcLj/+q//0tTURKFQQUFBQUFB+fn58mrveGKmiMViFxcXTU3NvLy8+fn5ysrKvXv3fv/992QyWTF3QEokkqmpqebm5ri4OFtbWzs7u4KCAhVfHQdQQ9Ayxjdv3qyurhaLxQr+fL5YpnR2dh5fZNeuXT/++GNSUpJcdshZOVOgbca/+eYbW1tbaEnOoaEhR0fHV199tays7IXXE5dKpSKRaHR0lMlkPmW0XCwWs9nskZGR9PT0K1euGBsb5+bmgnMTQGXRaLTk5GRTU1MymazgaaAXy5QlUlNTv/vuu88//xyHw62+pJUzhcvlYrHY//3f//Xz8yOTyUKhcGZmJicn55VXXnF0dKRQKC92MJFIRKVSdXR0kpKSVpwMh25cnpqaysvLO378uKamZm5u7guM5gKAgg0PD6PRaGtr66mpKUWeqtBotIsXL5qamq5ygefQ0NCtW7e6urquvqSVM2ViYsLa2vpPf/rT66+/vmXLlq1bt/79739/6623XnrppX/9618v3KjC4/HKysree+89W1vbFYfKWSxWbm7utWvXdHR0srKyRkdHuVyu6iw2AwBPIhKJBgcH9fX14+PjFTley2Qy4+Pj09PTV3kiHx8f/8UXX6xhpgwODm7ZsuXKlSspKSnYXz148MDe3v7NN99MTEx83jkXBoORn59/4cKFTz755JVXXtmyZYuGhgYcDoeSBVojNicnx8LCwsLCIiEhobOzk8FgqELjMwDIiM/nt7W1GRkZ5efnK2xSUiQSTUxMrHKzh9nZWW9v73/961/BwcGrL2mFTJmZmUlLS3vppZeSkpIWX3dwOBwsFvvGG284Ojo+1zKudDo9ISFBQ0PjT3/606Zfvfzyy++9956ZmVlVVVVJSYmLi4urq2tYWBjUw7b6NwYACiaVSoVCYUZGhrOzc3l5ucour0GhUIqKirBY7MLv7KysrL179/7nP//p6+tb/euvkCl9fX3Xr1//4IMPenp6FnejiEQiCoXy5ZdfnjhxorKyUsYDiMXiBw8eHD58eNNK3nnnnZ9//tnBwQEOh+fk5FAoFHClA6xfUql0dnY2PDzcz8+vvr5eNT/MVCo1ISHh9OnTHh4eKBQKhUJduHDhzJkzd+/elcvrr5Apg4ODSCTS09Nz+f4DAoEgMDDQ1ta2sbFRxgNMT0/b2tq+9tprK2bKpk2b3nzzzVu3bpFIJHAzMbAxjIyM+Pv7BwYGDgwMrPWxWCxWZ2cnHo9/ribSnp4enUWsrKyKi4vlVdKar3XQ2dl5/vz5JwXKpk2b3n77bTQarYLLfALAC2tsbESj0WFhYXLp+HgKPB5vaWmJQqFUZ3p0zTOluLj4hx9+eEqmvPbaa1paWoODgzMzM0wmk81m83g8Pp8vFAoV30EEAPLy8OFDBweH9PR0kUi0dh/j9vZ2TU3NVfanyNeaZ0pzc7OWltZTMmXz5s3bt29/8803d+zYceDAgWvXrsHhcAwGU1tbOzw8DNZDAdYpHo9XWFioq6vb2tq6dtf16pgpNBrNyMjo5ZdfflKmvPPOOzExMbW1tWVlZZmZmRERER4eHnZ2dhcvXjx27Nh//vMfLS0tY2NjFxeX2NjY/Pz8pqammZkZ1Rz9AoAFUql0fHw8LS1NR0dn7SYf1DFTBALBvXv3vv322xUD5Y033vj5558nJibEYjGPx2MwGCQSqbe3t6WlpaysLC8vLy0tLTo6OiQkxMfHx9nZ2c7Oztzc/MqVK5cuXbKysvL29o6Kirp//35bWxsej2ez2Wv9dgBAdiKRiEQi+fn5ubi4EInEtTiEOmbK/Pw8iUQKCgravXv38tHZn376qbS09OnfzmAwiERiV1cXFovNzc29d++en58fEolEIBBwONzNzc3V1dXFxcXZ2dnJyQmBQAQHBycmJpaUlFRUVPT3909MTIALKEBZBALBwMCAnZ1dYmLiC9/U8hTQD1diYqLqzHIoaI3r4eHh8PDwkydPfvrpp++///6uXbv27Nljbm5eXFz8Ypea0PpM7e3tWCw2MzPT398fiUSam5sbGhqam5vb2dm5urrC4XBfX9+QkJA7d+4kJycXFBTgcDjojIZCobDZbNCnCyiASCSqqKhwcHBYi5vX+Hw+hUKh0Wiqs4Sl4tbN5/F4eDw+JiYGiUSGh4cXFhauxdkgk8kcGhqqrq5OSEjAYDB2dnZXrlw5evSopqamrq7u9evXYTCYn59fVFRUbm4uDodraGiApveHh4cnJyeZTKZq7rMNrHfR0dGenp5YLFZl+2vlZQPuQ7ii8fHxurq6nJwcX19fOzu7S5cuff311x9++OGXX36pra1tYmLi4uISHx9fWFjY0dExOjpKo9EmJydnZmZYLBaPxxMKheCkBlgNgUDg4+ODQCC6u7s39mdJXTIFWkVBLBaLRCKhUCgQCObm5mZnZ/v7+wsKCqKiouBwuI6OjoaGxtatW994442PP/74+PHjt2/f9vPzy83N7e3tXd5VDACyk0qlNBrNy8vr1q1bG3sxIHXJlBVJJBKBQMBms2dmZiYnJykUysjISH9/f1tbW2lpaUpKCgqFsre3v3r16o8//vj5559/+eWXP//88/Xr1/38/DIyMioqKggEArilAJCRSCTq7Oz08/ODwWDyek0ikejn55eWliavF1w9tc6UJxGJRGw2e3JycmhoqLe3t6mpCYfDFRUVZWVlRUVFBQcHu7u729nZmZqaXr58WUtL69KlS7dv3w4KCoqLiysrK+vp6aHRaMp+E4Aq4nK51dXVMBgsPj5eLtORXV1dFy5cgMPhq38peQGZ8hzm5ubGxsaGhoaamppKS0tzcnLi4+ODg4P9/Pw8PT0RCAQMBnN0dLx165aNjY2NjQ0SiQwKCkpPT3/48GFLSwuZTH7hZTeBDYPBYBQVFZmZmdXV1a3+8wD1p9jb28ulNrkAmbJaYrGYyWQODAzU1dWVlJQkJiYGBga6ublZWFjY2treunXL2dnZzc3Nw8PDx8fH398/JCQkPT39wYMHFRUVHR0dBAJBdbqVAMWYmJjAYDAODg7d3d2rnAYCmaJGhEIhmUzu7u7Oy8uLi4vz9va2sLC4cOHCiRMn9PX1zczMbt++7enpGRISEhcXl5+fX1xcXFNT097eDu0Ix2Aw1ulevMAzSSSS6elpa2vrsLCwwcHB1bTtg0wB5kUiUUtLCxaLjY+Pd3d3NzMz09LS2rFjx+eff37y5EkjIyN7e/vAwMDs7OyHDx8+evRoaGiISCRSqVQ6nT4zM8Plctf0PldAMcRi8djYmKGh4b1791az+XlPT88vv/zi6ekpx9pWCWSKSpBIJDMzMw0NDUlJSb6+viYmJvv27fvkk082b9784Ycffv/99wYGBkgkMioqqqqqikKhQGtBiEQisVgsFoslEgnYf349qqurs7S0TE5OfuGOFTab3dXVRSAQ5FvYaoBMUQlQ+8zc3ByHw2EymQwGY3x8nEqlkkik+vr6goKC0NBQR0dHExOT48eP7969e9u2bUeOHNHX13dycsJgMAUFBY2NjaADeN2Zm5tLTU1FIBAFBQUv9gpQP4TqNObPg0yRu9HR0cDAQC0tLT8/v+Vf5XK5DQ0Nx48fNzMzk3FLEx6PNzs7C8039fX1tbS01NTUYLHY5OTkiIgIb2/v27dvm5qa6urqHjp06NSpU4aGhjAYLDQ0NC0traOjg0gkglsoVdnk5OSdO3fc3d07OzuVXYt8gEyRp6ysLGNj4507d7799tvGxsZLvorH4+Fw+JEjRzZv3vztt9+ucs83Op1OJBJ7e3sbGhqgdSHu3r0bERERGBjo7e3t7u7u7OxsbW0N3Vdpa2uLQCAwGEx+fn5VVVVfXx+dTgfdeioCj8eHhYXB4fCJiYkNcAELMkU+pFJpW1ublpbWyZMnjx49+vHHHy/JFAqFEhAQ8MUXX+jr6//zn//ct2+fXPaRXILL5Y6NjXV1dVVXV+fn52MwGH9/f2dnZwcHBycnJxcXFxgMBofD3d3doTXTIyIi0tLSCgoKamtr+/v7R0ZGlLKRuJoTi8UtLS0eHh4hISHPe7s8gUDIysqqr69fu/KeF8gU+ZBKpaWlpZaWlllZWbGxsUeOHFmSKf39/cHBwXZ2dgQCQVtb+8iRI2uRKU/CYDCGhoZqamqSk5MjIyPhcPj169cvXbqkp6dnYWFx69YtOBwO9c4kJCRkZWUVFhZWVVW1t7f39PRQqdSZmRkwWLOmeDxefX29sbFxXl7ec90NVFRUpK2t7eXltXa1PS+QKfKXkZGxPFMWsFiss2fPKjhTnoRMJtfU1OTk5ISGhtra2pqYmBw8eFBDQ+PEiRPXrl2zt7eHwWBxcXH379+vrKyEemcGBgbGxsYmJiZmZ2fn5uY29i22isRkMktKSi5cuNDc3Cz72SLIFLWwjjJlRSwWC4/HQ5NNKBTq7Nmz33///bvvvvvBBx/s27dPW1vbzc0tODg4Ozu7s7OTRqNBK0JwOBwejycQCMC6EC+MzWYHBwc7ODh0dHTI2AgHMkUtrPdMkUqlYrFYIBDweDwul8tisWZnZ6enp/v7+3E4XEZGhouLi7m5+ZkzZz755JO///3vu3bt0tbWNjIyQiKRGRkZ1dXVVCpV2W9iXZJKpTwez8LCIjw8XMaWE5ApamG9Z8qTCIVCaF2I0dFRIpHY39/f2dnZ2NhYUlISHx8fGhrq5uZmamr6888///DDDxoaGqdPn75+/bqvr290dDQWi3306BGdTlf2m1gHBgcHb968GRUVJcs/F8gUtbBRM2VFEomEy+XSaLSRkZHu7u7a2try8vKcnJx79+5FR0cHBQV5eHi4urpaWVkZGxvr6ur+8ssvDg4OKBQqOTm5sLCwqakJagtW9vtQIWKxuLS0FIFAJCUlPfNfhkqlVldXP3r0SDG1yQJkivypVaY8iVAonJ6eJhAIjY2N0BVTdHR0QEAAAoFwd3eHw+EwGGxhwwNnZ2cEAhEdHZ2enl5cXNzc3Dw4ODg1NaXsN6E0TCYzIyMDiUQWFhYqu5bnBjJF/kCmPAWPxxsZGenq6srPz09KSgoJCXFycjI1NTU0NLSysrK3t3dxcUGhUH5+fqGhobGxsenp6fn5+TU1Na2trYODg5OTk1wuV9lvQhEoFEp8fDwMBuvp6VlfjXAgU+RDKpWOjY01NjZWVFTA4fCvvvrq5MmTFRUVFRUVExMTIpFodnb20aNHFRUVRUVF+/bt++qrrwIDAysqKnp6ekDvvEQiYTKZra2tJSUl9+7d8/LysrGx+fnnnw8cOHD69OkrV67Y2NjAYLCgoKCkpKS8vLzKysrm5uaOjo7BwUEKhTI5OclisTbe7dp9fX3BwcEIBGJycvJJ00BCoZDD4ajUxSPIFPmQSqWJiYkaGhpblsnNzWWz2S0tLdevX1/+VUNDQ7DQ5JMIBAIikdjQ0HDv3j1/f/8bN24cP378s88+e/fdd/ft23fmzBkrKytfX9/4+PiHDx9C2zZNTExAi0Kw2Ww+n7/eW/V6enpMTU3j4+MZDMaKM/Q0Gq22travr0/xtT0JyBT5WJh/nVtGLBZDtx0LhcLlXxUKhRvst6scSaXSFTc8gDK6uLg4MDDQ0tLy/Pnz33zzzVtvvfXnP/9ZQ0Pj0qVLN2/exGAw5eXlHR0dyn4TqyIQCLq7uzU0NCorK1fcure4uPj8+fM+Pj6Kr+1JQKYA649UKuXz+RwOh8Fg0Gg0CoUyPDzc19fX0dGRk5MTFRXl5eVlaWmpo6Nz7NixnTt37t+//6effnJ0dAwJCUlLS2ttbR0bG1ujTdHlSyqVcjgcLBarp6dXXV29/LQLzCUDwFqBThWnp6fHxsYIBEJXV1d9fX1lZWVeXl5KSkp0dDQajYbBYDdv3tTX179w4cLJkydNTU0dHR2DgoIyMzOhsS0ej6dqTcASiYTNZkPrITQ2Ni75KsgUAFA0qVTKYrGoVGpPTw+0LkRaWtrdu3eDgoJ8fHygDQ9cXFygDQ+srKxu3rzp7e0dHR2dkZFRXl7e19dHoVCUvi4EiURCo9Hh4eFLWlFApgCACqFSqf39/XV1dffv34+LiwsICLCzs7OysrKzs7t9+za04YGnp6ePj09gYOCdO3egPr36+vrOzk4KhTIzM6PIBdaampp8fHyio6MX3/qAw+EMDAzCwsIUVsYzgUwBgN/g8XgEAqGuru7BgwdRUVFOTk43btw4c+bM2bNnr169amFh4erq6uXlhcFgkpKScnJyysvL6+vr29vbBwYGKBTK1NTU3NzcGo275+fne3h4ZGRkLDTp9Pf3JyYmVlRUrMXhXgzIFACQCZ1O7+3thW7XhsPhurq6hw8f3r179549e86fP29iYuLu7h4WFpaamlpfX//o0SMCgUChUMbHx6emplgsFo/HW/2oMJ/Pz8jIsLa2rqurE4lEdDqdQqGQSCSoSUdFugFBpgDAqoyMjJSXlyckJDg7O1+7du3IkSNbtmz5y1/+snPnzlOnTpmbm8Ph8Pv379fV1Y2PjwuFwiUbHkDz5bIfjsFgJCUlnTp1ikQieXl5nTp1au/evSdPnnR0dKysrIQaF9buzcoCZAoArIpIJOLz+dAd23Q6fWJigkKhDAwMVFdXJycn+/v7u7i4XLhw4fDhw//+979379599OhRPT09b2/vO3fulJeXEwiE59rhVCwW9/b2Wlpavvfee3/5y19effXVP/zhD6+++uqf//znXbt2hYSEKP1sBWQKAMifWCzmcrlTU1MUCoVAIHR2djY3N1dVVeXn50PLd7q7u9++fdvQ0PDs2bOHDx8+c+aMhYWFm5tbTExMcXFxY2MjlUpdcQCYz+cXFBTs2rXrd7/73abfeuWVV3bs2HH//v3Z2VnFv+UFIFMAQHH4fD6dTieRSO3t7fX19cXFxenp6bGxseHh4X5+fl5eXjAY7Pbt27a2tmZmZiYmJjdv3vTz80tISMjOzm5paSEQCDU1NdbW1n/4wx82reT3v/+9lpZWf3+/Et8jyBQAUD42mz08PNzV1VVWVpaenh4TE+Pj4+Pk5OTo6Ojs7Ozq6urq6gqHwxEIhIGBwc6dO1cMlE2bNv3ud7978803a2pqlNglDDIFAFSUUCicmprq7Ox8+PBhZmamr6+vo6PjsWPH/vjHPz4pUyCFhYVKvNkdZAoArCepqak7dux4SqC89NJLRUVFIFMAAJBJWVnZkSNHnn7t09TUpMQKQaYAwHpCJBLd3NyelCm///3vL168ODg4qMQKQaYAwHoiEAhqa2tPnz69PFD+8Ic/7N69u7GxUbkb1IJMAYB1hslk4nA4IyOjf/zjH5s3b4ZOT7Zt26anp1dYWMjlcp/USovH49Fo9E+/lZOTw2Aw5FgeyBQAWH/4fH57e3tUVJS7uzu0BW10dHRjY+PTF+Wtqak5derUrl277O3tPTw8PDw8Dh06pKWllZWV9Vy9vE8HMgUA1jE+nz8zMyNjIkCZcv78+bGxMeiRlJSUjz/+2NLScmRkRF4lgUwBAHWxPFPIZPKhQ4cuX77c3Nwsr6OATAEAdbE8U/B4/L59+/T09Do7O+V1FJApAKAulmeKh4fHtm3bfH195bgKL8gUAFAXUKb86U9/+uCDD3bs2LFjx46//vWv58+fl+8ycSBTAEBdQJmioaERHx+fl5eXl5cXGxurqan5008/5eXlyesoIFMAQF0sv/ZhsVgwGOyLL76ws7NjMplyOQrIFABQF8szZX5+PjMzc8+ePZcvX168HP9qgEwBAHWxPFN4PJ6/v//XX39tbm4ur25akCkAoC6gTDl69GhlZWVfX19fXx8Oh/vhhx/27t177949eR0FZAoAqIva2lptbe3f/9aJEyfKy8vleBSQKQCgLubm5iYnJ0m/NTExwefz5XgUkCkAAMgTyBQAAOQJZAoAAPIEMgUAAHkCmQIAgDyBTAEAQJ5ApgAAIE8gUwAAkCeQKQAAyBPIFAAA5On/A92YwgjZbScaAAAAAElFTkSuQmCCAA==
A.12km B.13km
C.14km D.15km
【分析】本题与悟空二郎神一题其实是一种题型。根据题中要求,求的是距离河岸1米处的某点距离A、B的最短距离。根据上道例题的启示,我们要把A、B两点放在同一线段上,先画一条与河岸平行且距离河岸是1米的线,以该线为对称轴做B点的对称点B,连接AB,与平行于河岸的线相交于O点,小伙伴们请注意对称的距离是4千米,BB之间的距离就是8千米。再过A点做BB的垂线AP,垂足是P,可知BP为1千米,BP的长度就是8-1=7千米,在直角三角形ABP中,根据勾股定理
http://www.huatu.com/2017/0708/data:image/png;base64,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
,所求的最短距离AOB,就是AB的长度。同样的在直角三角形ABP中,根据勾股定理,斜边AB的长度就是
http://www.huatu.com/2017/0708/data:image/png;base64,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
,因此本题应该选择B选项。
http://www.huatu.com/2017/0708/data:image/png;base64,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
可见只要明白定理,理解考点,我们也能够解出题目的。特别是几何问题在国考中这么重要,国考真题在我们知道考点、了解几何基础知识的基础上是比较容易解出的。
《择天记》中陈长生聪明绝顶还争分夺秒地学习知识,他身边有师傅商行舟、师兄余人、徒弟落落、朋友唐棠和轩辕破,他们一起经历磨难共同成长;《楚乔传》中楚乔从婢女到谍者到将军王爷最后到皇妃,她不停地锻炼自己、积蓄力量,她身边有宇文玥、元崇、燕洵、萧策、誓死追随的下属一起经历成长。华图就是你成公路上的师傅和随行人。我们面临国考,虽不用逆天改命,也不必整天担心生死,但我们也要努力,成功是会倾向有准备的人的,更何况你还有华图在你们身边一直陪着你奋斗呢!我们一起加油!
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