Chapter 9, Problem 16CT

To determine

To find: the value of angle P .

Answer to Problem 16CT

The angle $m\angle P$ is 40.

Explanation of Solution

Given:

The circle is shown below:

Arcs RS and ST are 120 and 160 respectively.

Calculation:

For circle with intersecting tangent and secant as shown below:

The angle formed by the tangent secant is,

  $\angle 1=\frac{1}{2}\left(arcBC-arcAC\right)$

For given circle,

The arc $RT$ is calculated as follows:

  $\begin{array}{c}arcRT=360-\left(arcRS+arcST\right)\\ =360-\left(120+160\right)\\ =80\end{array}$

The angle $m\angle P$ is calculated as follows:

  $\begin{array}{c}m\angle P=\frac{1}{2}\left(arcST-arcRT\right)\\ =\frac{1}{2}\left(160-80\right)\\ =40\end{array}$

Hence, the angle $m\angle P$ is 40.