Question

in an isosceles triangle ABC with the bisectors of angle B and angle C intersect each other at o join a to o show that o b is equals to OC AO bisects angle A

Answer 1

i) It is given that in triangle ABC, AB = AC

∴ ∠ACB = ∠ABC (Angles opposite to equal sides of a triangle are equal)

∴ 1/2 ∠ACB = 1/2 ∠ABC

∴ ∠OCB = ∠OBC

∴ OB = OC (Sides opposite to equal angles of a triangle are also equal)

(ii) In ΔOAB and ΔOAC,

AO =AO (Common)

AB = AC (Given)

OB = OC (Proved above)

Therefore, ΔOAB ≅ ΔOAC (By SSS congruence rule)

∴ ∠BAO = ∠CAO (CPCT)

∴ AO bisects ∠A.