如图,△ABC内接于圆O,AD垂直于BC于点D,AE是圆O的直径,试证明:AB*AC=AD*AE
人气：382 ℃ 时间：2019-08-16 23:23:32
解答
证明：AE为直径
所以∠ABE=90度
因为AD垂直BC
所以∠ADC=90度
因为∠ABE=∠ADC,∠E=∠C(都是弧AB对的圆周角）
所以△ABE∽△ADC
所以AB/AD=AE/AC
所以AB*AC=AE*AD
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