Question

In an isosceles triangle ABC with AB=AC,BD is perpendicular from B to the side AC. Prove that BD(square) - CD(square)=2CD*AD.

Answer 1

Proof : In right triangle ABD,

AB2 = AD2 + BD2

[Using Pythagoras theorem]

But AB = AC

⇒ AC2 = AD2 + BD2

⇒ (AD + DC)2 = AD2 + BD2

⇒ AD2 + DC2 + 2AD.DC = AD2 + BD2

⇒ 2AD.DC = BD2 - DC2

⇒ BD2 - DC2 = 2AD.CD.