In △ ABC, ACB is 90 ° and CD ⊥ AB is made at d through point C. e is the midpoint of BC. Connect ed and extend the extension line of intersection CA to F. verify: AC / DF = BC / CF In △ ABC, ∠ ACB = 90 °, make CD ⊥ AB at d through point C, e is the midpoint of BC, connect ed and extend the extension line of intersection Ca at F. verification: AC / DF = BC / CF

In triangle BCD, de = CE = be, angle EBD = angle EDB = angle ADF
Double vertical, so angle FCD = angle EBD
So, angle FCD = angle FDA, so triangle fad is similar to triangle FDC
FD / FC = ad / DC and AD / DC = AC / CB
Therefore, AC / CB = FD / FC
Therefore, AC / DF = BC / CF

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