Chapter 10.1, Problem 1PSA

a)

To determine

To Prove: That $\Delta AOB$ in an isosceles

Explanation of Solution

Given:

Chord AB is the cord of a circle.

  

Proof:

  $\begin{array}{l}OA=OB.\text{ Radius of circle}\text{.}\\ \text{Two sides are equal }\Delta \text{AOB is isosceles}\text{.}\end{array}$

b)

To determine

To Prove : That $\angle A\cong \angle B$ in the given figure

Answer to Problem 1PSA

Explanation of Solution

Given:

AB is chord.

  

Proof :

  $\begin{array}{l}OC\perp AB,\text{ bisects AB}\text{.}\\ \text{AC}=BCandOA=OB,OC\text{ is common}\text{.}\\ \Delta \text{OCA and }\Delta \text{OBC are congruent}\text{.}\\ \text{Therefore, }\angle A=\angle B\end{array}$