Chapter 10.6, Problem 28PSC

To determine

To Prove : Triangle SIT is isosceles.

Explanation of Solution

Given Information :

1) It is tangent to the circle.

2) It is bisector of angle ATM

Formula Used :From alternate segment theorem.

Calculation:

  

  $\begin{array}{l}\text{From Alternate Segment Theorem,}\\ \angle \text{ITM}=\angle A\\ \angle 1=\angle 2\text{(Since, TS is besector of angle ATM)}\\ \text{Therefore, }\angle ITM+1=\angle A+\angle 2\\ \angle ITS=\angle S\\ \text{Since, }\angle \text{A + }\angle \text{2}=\angle S\text{ (from exterior angle theorem)}\\ \text{Therefore, IS = IT}\\ \text{So, triangle SIT is isoscels}\text{.}\end{array}$