Chapter 5.3, Problem 16PSB

To determine

To Prove: $△OSP\text{is isosceles}\text{.}$

Explanation of Solution

Given:

  

  $\overline{NR}\parallel \overline{PS}$

Concept Used:

When parallel lines is intersected by a transversal corresponding angles are equal.

Proof:

Here, we have, $\overline{NR}\parallel \overline{PS}$

  $\begin{array}{l}\text{In }△ORN\text{and }△OSP\\ \Rightarrow \angle R\cong \angle S\\ \Rightarrow \angle N\cong \angle P\\ \because \angle R\cong \angle N\left(\because \overline{ON}\cong \overline{OR},\text{raddi of circle}\right)\\ \Rightarrow \angle S\cong \angle P\\ \Rightarrow △OSP\text{is isosceles}\text{.}\end{array}$