Chapter 4.1, Problem 15PSB

To determine

To Prove: AO bisects BC.

Explanation of Solution

Given information: $\angle B=\angle C.$

Formula Used: properties of circle, Congruency of triangles.

Proof:

  $\begin{array}{l}\angle B=\angle C\left(Given\right)\\ \therefore AC=AB\left(Sidesoppositestoequalanglesareequal\right).\\ \therefore OB=OC\left(Eachequaltoradius\right)\\ OA=OA\left(Common\right)\\ \Delta OAB\cong \Delta OAC(SSS)\\ \therefore \angle OAB=\angle OAC(CPCT)\\ \therefore \Delta ABE\cong \Delta ACE(ASA)\\ \therefore BE=CE(CPCT)\end{array}$