Question

If ABC is an isosceles triangle and D is a point of BC such that AD ⊥ BC, then

Options

• AB² − AD² = BD.DC

• AB² − AD² = BD² − DC²

• AB² + AD² = BD.DC

• AB² + AD² = BD² − DC²

Answer 1

Given: ΔABC is an isosceles triangle, D is a point on BC such that `AD ⊥ BC`

We know that in an isosceles triangle the perpendicular from the vertex bisects the base.

∴ BD = DC

Applying Pythagoras theorem in ΔABD

`AB^2=AD^2+BD^2`

`⇒ AB^2-AD^2=BD^2`

`⇒ AB^2-AD^2=BDxxBD`

Since `BD =DC`

`⇒ AB^2-AD^2=BD xxDC`

Hence correct answer is `a`