Question

Angle  ABC= angle BAC,D and E are points on BC and AC such that DB=AE. If AD and BE intersect at O then prove that OA=OB

Answer 1

In triangle ABC , angleABC =angleBAC.

So in triangles ABE and ABD angleABD =angleBAE

Again AE=BD (given) and AB is common.

Hence by SAS rule triangles ABE and ABD are congruent.

So we get angle BAD= angle ABE or  angle BAO= angle ABO in triangle ABO. This means OA=OB