Question

In an equilateral triangle ABC, D is a point on side BC such that BD = BC. Prove that 9 AD² = 7 AB².

Answer 1

Let the side of the equilateral triangle be a, and AE be the altitude of ΔABC.

∴ BE = EC = =

And, AE =

Given that, BD = BC

∴ BD =

DE = BE − BD =

Applying Pythagoras theorem in ΔADE, we obtain

AD² = AE² + DE²

⇒ 9 AD² = 7 AB²