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Question

In the given figure, ACB=90o and CDAB.

Prove that BC2AC2=BDAD.

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Solution

On ABC and ACD

ACB=CDA,
CDA=CAB

ΔABC and ΔACD are similar

ACAB=ADAC

AC2=AB×AD

Similarly, ΔBCD and ΔBAC are similar.

BCBA=BDBC

BC2=BA×BD

BC2AC2=AB×BDAB×AD

BC2AC2=BDAD


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