Question

In right-angled triangle ABC is which ∠C = 90°, if D is the mid-point of BC, prove that AB² = 4 AD² − 3AC².

Answer 1

∆ABC is a right-angled triangle with ∠C = 90°. D is the mid-point of BC.

We need to prove that.

Join AD.

Since D is the midpoint of the side BC, we get

BD = DC

∴

Using Pythagoras theorem in triangles right angled triangle ABC

.....(1)

Again using Pythagoras theorem in the right angled triangle ADC

.....(2)

From (1) and (2), we get

Hence, .