燕子猫咪
春芽
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延长FP交AD于Q.
△GPQ与△CPF相似,PG:PC = GQ:FC
GQ = GD-QD = GD-BF (△OBF和△ODQ全等,所以QD=BF)
现在解BF FC长度.设正方形边长为a,BF长度x
由于AF是角平分线,由F向AC作垂线交AC于K, 有BF = FK = x
角ACB是45度,那么FC = 根号2*x
BF+FC = a, 即x+根号2*x = a, 得 x = a/(根号2+1)
代回去第一部分,PG:PC = GQ:FC = GD-BF:FC = a/2 - x : 根号2*x = 1/2 - (根号2)/4
1年前
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