Question

In ∆ABC, ∠ABC = 135°. Prove that AC² = AB² + BC² + 4 ar (∆ABC)

Answer 1

We have the following figure.

Here is a right triangle right angled at D. Therefore by Pythagoras theorem we have

Again is a right triangle right angled at D.

Therefore, by Pythagoras theorem, we have

Since angle ABD is 45°and therefore angle BAD is also 45°.

Hence AB = DB

So,

Since

So,

Hence we have proved that