来自程裕霞的问题
已知,AB,CD是⊙（O,6cm）中互相垂直的弦,并且AB把CD分成3cm和7cm的两部分,求现AB的长和他的弦心距
已知,AB,CD是⊙（O,6cm）中互相垂直的弦,并且AB把CD分成3cm和7cm的两部分,求现AB的长和他的弦心距
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2020-06-26 09:18
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黄青
做OE⊥ABE为垂足
做OF⊥CDF为垂足设AB和CD的交点为M
CF=DF=0.5CD=5
MF=CF-CM=2
而四边形OEMF为矩形
OE=MF=2(弦心距)
AE=√OA²-OE²=4√2
AB=2AE=8√2
2020-06-26 09:21:26
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