If ABC is an isosceles triangle and D is a point on BC such that , then

Question

Philoid · Accepted Answer

Given ABC is an isosceles triangles and AD ⊥ BC.

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

∴ BD = DC

We know that the Pythagoras theorem state that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Now, in right triangle ABD,

⇒ AB² = AD² + BD²

⇒ AB² – AD² = BD²

⇒ AB² – AD² = BD (BD)

Since BD = DC,

∴ AB² – AD² = BD (DC)

If ABC is an isosceles triangle and D is a point on BC such that, then