题目内容
如图,已知菱形ABCD的边AB=10,对角线BD=12,BD边上有2012个不同的点
,过
作
于
,
于
,则
的值为______
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19315.2
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作点E1关于BD的对称点M,则P1M⊥BC,
又∵P1F⊥BC,
∴M、P1、F1在一条直线上,且MF1⊥BC,
故可得PiEi+PiFi等于菱形两边BC与AD之间的距离,
又∵AO=
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∴BN=
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故可得:P1E1+P1F1+P2E2+P2F2+…+P2012E2012+P2012F2012=2012×9.6=19315.2.
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