Question

A and B are points on a circle with centre O. C is a point on the circle such that OC bisects angle AOB, prove that OC bisects the arc AB.

Answer 1

answer along with explaination is given.

Answer 2

Answer:

The proof is explained step-wise below :

Step-by-step explanation:

For better explanation of the solution, see the attached figure :

To prove : OC bisects the arc AB

Proof : In ΔCOA and ΔCOB,

OA = OB (Radius of the same circle)

∠COA = ∠COB ( OC bisects the angle AOB)

CO = CO ( Common side)

By SAS postulate of congruency of triangles, ΔCOA ≅ ΔCOB

Now, AC = BC ( Corresponding parts of congruent triangles are equal )

Therefore, OC bisects the arc AB

Hence Proved.