Chapter 4.4, Problem 1PSA

To determine

To Verify: $OM\perp AB.$

Explanation of Solution

Given information: M is midpoint of AB.

Formula used: congruency of triangles, linear pair axiom.

Proof:

  $\begin{array}{l}\text{M is midpoint of AB}(\text{given})\\ \therefore AM=BM.\\ \text{Join}OA\text{and}OB.\text{(Each equal redius)}\\ \therefore \Delta OMA\cong \Delta OMB(\text{SSS})\\ \therefore \angle OMA=\angle OMB(CPCT)\\ \angle OMA+\angle OMB={180}^{\circ }(\text{Linear pair axiom})\\ \therefore \angle OMA={90}^{\circ }=\angle OMB\end{array}$