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Question

In ΔABC, BDAC, DAC and B is a right angle. If AC=5CD then show that BD=2CD.

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Solution

From the triangle BDC.
BC2=BD2+x2...(i)
and
From the triangle ABD
AB2=BD2+16x2...(ii)
From the triangle ABC
AB2+BC2=AC2...(iii)
Thus substituting in (iii) from (i) and (ii),
BD2+x2+BD2+16x2=(25x2)2BD2=8x2BD2=4x2BD=2x
hence
BD=2CD




1166558_879207_ans_6606468d0eaf4a63b4337376d9b257d9.jpg

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