Chapter 10.5, Problem 34PSC

To determine

To Find : The measure of the arc made by secant on other side of tangent.

Answer to Problem 34PSC

$132°$

Explanation of Solution

Given information :

1) $\angle P=38°$

2) $\stackrel{⌢}{AC}=2\stackrel{⌢}{AB}$

Formula Used: The angle between a secant and a tangent is equal to half the difference of the enclosed arc.

  $\begin{array}{l}\frac{1}{2}\left(\stackrel{⌢}{AC}-\stackrel{⌢}{AB}\right)=\angle P\\ \frac{1}{2}\left(2\stackrel{⌢}{AB}-\stackrel{⌢}{AB}\right)=38°\\ \stackrel{⌢}{AB}=76°\\ \stackrel{⌢}{AC}=152°\\ \text{Now}\stackrel{⌢}{AB}+\stackrel{⌢}{AC}+\stackrel{⌢}{BC}=360°\\ 76°+152°+\stackrel{⌢}{BC}=360°\\ \stackrel{⌢}{BC}=132°\end{array}$