Question

In an isosceles triangle abc with ab = ac, bd is perpendicular from b to the side ac. Prove that bd^2 -cd^2 = 2cdad

Answer 1

proof: In right triangle ABD,

AB² = AD²+BD²

[Using Pythagoras theorem]

But,. given, AB = AC

AC²= AD² + BD²

(AD + DC)²= AD² + BD²

AD² + DC² + 2AD.DC = AD² + BD²

2AD.DC = BD² - DC²

BD² - DC² = 2AD.CD

Hence proved..

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