Question

In triangle abc ad perpendicular bc such that (ad square ) =bd×cd prove that abc is aright angle at a

Answer 1

InΔABC,AD⊥BCand AD²=BD.DC

Now,

InΔABD,AB²=AD²+BD²→.1

InΔADC,AC²=AD²+CD²→.2

(1)+(2)

AB²+AC²=2AD²+BD²+CD²

AB²+AC²=2BD.DC+BD²+CD²

[Given,AD²=BD.DC]

AB²+AC²=(BD+CD)²

AB²+AC²=BC²

So, according to the PYTHAGORAS THEOREM ∠BAC=90°.

HENCE PROVED

Answer 2

Answer:

Check your answer please