Question

In an isosceles triangle ABC, with AB=AC , BD is perpendicular from B on AC. prove that BD^2+CD^2=2AC*CD

Answer 1

An isosceles triangle ABC, with AB = AC. BD is perpendicular from B to the side AC.

To Prove: BD2 - CD2 = 2CD.AD

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.

Answer 2

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