Question

In an isosceles triangle ABC with AB = AC, BD is perpendicular from B to the

side AC. Prove that

BD2

– CD2 = 2CD . AD.​

Answer 1

Answer

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

Answer 2

Answer:

given-:

In the isosceles AABC, AB = AC and BD is the altitude through B.

to Prove that

BD2-CD2 = 2CD. AD.