In an isosceles ∆ABC, AB=AC and the bisectors of ∠B and ∠C intersect each other at O. Also, O and A are joined.

Question

In an isosceles ∆ABC, AB=AC and the bisectors of ∠ B and ∠ C intersect each other at O. Also, O and A are joined. Prove that: (i) OB=OC (ii) ∠ OAB= ∠ OAC

Philoid · Accepted Answer

From the given figure, we have:

(i) In ∆ABO and ∆ACO

AB = AC (Given)

AO = AO (Common)

∠ ABO = ∠ ACO

∴ By SAS congruence rule

OB = OB (By CPCT)

(ii) As, By SAS congruence rule

∆ABO ≅ ∆ACO

∴ ∠ OAB = ∠ OAC (By Congruent parts of congruent triangles)

Hence, proved

In an isosceles ∆ABC, AB=AC and the bisectors of ∠B and ∠C intersect each other at O. Also, O and A are joined.Prove that: (i) OB=OC (ii) ∠OAB=∠OAC

In an isosceles ∆ABC, AB=AC and the bisectors of ∠B and ∠C intersect each other at O. Also, O and A are joined.
Prove that: (i) OB=OC (ii) ∠OAB=∠OAC