Question

In an isosceles triangle ABC, with AB = AC, the bisectors of ∠B and ∠C intersect each other at 0.

Join A to 0. Show that
(i) OB = OC

(ii) AO bisects ∠A​

Answer 1

its the answer........

Answer 2

Given:

AB = AC and

the bisectors of ∠B and ∠C intersect each other at O

(i) Since ABC is an isosceles with AB = AC,

∠B = ∠C

½ ∠B = ½ ∠C

⇒ ∠OBC = ∠OCB (Angle bisectors)

∴ OB = OC (Side opposite to the equal angles are equal)

(ii) In ΔAOB and ΔAOC,

AB = AC (Given in the question)

AO = AO (Common arm)

OB = OC (As Proved Already)

So, ΔAOB ≅ ΔAOC by SSS congruence condition.

BAO = CAO (by CPCT)

Thus, AO bisects ∠A.

Hope it helps !!!