Chapter 10.4, Problem 4PSA

To determine

To Prove : $S\left|\right|M$

Answer to Problem 4PSA

1

Explanation of Solution

Given information : $\begin{array}{l}\overrightarrow{AC}\text{ is diameter of circle with centre B}\text{. }\\ \text{Lines n and m are tangetns to A and C}\text{.}\end{array}$

  

  $\begin{array}{l}\text{We know that, line joining from centre to point of contact is}\\ \text{perpendicular to tangent}\text{.}\\ \Rightarrow \angle \text{SAB}\cong 90°\\ \text{Also, }\angle MCB=90°\\ \Rightarrow \angle SAB\cong \angle MCB\\ \Rightarrow N\text{ is parallel to M}\\ \Rightarrow \text{N || M}\end{array}$