Chapter 9, Problem 21CR

To determine

To complete: the blank in the given statement.

Explanation of Solution

Given information:

The given statement is “If $PH$ is a tangent, the arc length $GH=90$ and $m\angle GPH=25$ , then arc length $FH=$$\underset{\_}{}$ ”.

  $\overleftrightarrow{RS}$ is tangent to circle $N$

The given figure is as follows:

  

From the given diagram,

  $\begin{array}{l}m\angle GPH=\frac{1}{2}m(GH)-\frac{1}{2}m(FH)\\ 2(m\angle GPH)=m(GH)-m(FH)\\ m(FH)=m(GH)-2(m\angle GPH)\\ =90-50\\ ={40}^0\end{array}$

Hence,arc length $m(FH)={40}^0$ .