Question

In an isosceles triangle ABC with AB = AC ,BD is perpendicular from B to side ACso that BD²- CD²=2CD×AD .

Answer 1

Solution:-

Using Pythagoras theorem:

AD² + BD² = AC²   (= AB²)----------(1)

CD² + BD² = BC²                 ------- (2)

(2) -  2 × (1)  =>

=>  CD² - BD² =  BC² - 2 AC² + 2 AD²

=>                   =  BC² - 2 (AD +CD)² + 2 AD² 

=>                   =  BC² - 2 CD² - 4 AD × CD

=>                   =  BD² + CD²  - 2 CD² -4 AD × CD

=>                   = BD² - CD² - 4 AD × CD

Simplify to get 

     BD² - CD² = 2 AD × CD

=============

@GauravSaxena01