Question

In a ΔABC, it is given that AB = AC and the bisectors of ∠B and ∠C intersect at O. If M is a point on BO produced, prove that ∠MOC = ∠ABC.

Answer 1

Given that in, ΔABC

AB=AC and the bisector of ∠B and ∠C intersect at O and M is a point on BO produced

We have to prove ∠MOC=∠ABC

Since,

AB=AC ⇒ ΔABC is isosceles

⇒ ∠B = ∠C (or) ∠ABC=∠ACB

Now,

BO and CO are bisectors of ∠ABC and ∠ACB respectively

Equating (2) and (3)