In an equilateral triangle abc , d is a piont on side bc such that bd=1/3bc . Prove that 9ad*ad=7ab*ab

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

Let the side of the equilateral triangle bea, 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 obtainAD²= AE²+ DE²⇒ 9 AD²= 7 AB²