Chapter 4, Problem 7RP

To determine

To Verify: $OM\perp AB.$

Explanation of Solution

Given information: M is a midpoint of AB.

Formula Used: Congruency of triangle, linear pair axiom, properties of triangls.

Verification:

M is midpoint of AB (given)

  $\begin{array}{l}\therefore AM=BM.\\ OA=OB\left(\text{Each equal to radius}\right)\\ OM=OM\text{(Common)}\\ \Delta OAM\cong \Delta OBM(\text{SSS})\\ \Delta OMA\cong \Delta OMB(\text{CPCT})\\ \text{By linear pair axiom,}\\ \angle OMA+\angle OMB={180}^{\circ }.\\ \therefore \angle OMA={90}^{\circ }=\angle OMB\\ \therefore OM\perp AB\end{array}$