Chapter 15, Problem 20CR

a.

To determine

To find: the angle of CD .

Answer to Problem 20CR

  $RS=16$ .

Explanation of Solution

Given:

  $BD$ is the diameter.

  

Calculation:

According to the question, there is a circle in which $BD$ is the diameter and $AB={10}^{\circ },\angle C={40}^{\circ },\angle GFC={80}^{\circ }$ .

The objective is to find CD .

Now, let $ED=x,CD=y,BC=z$ , then

  $\begin{array}{l}\frac{y+10}{2}={60}^{\circ }\\ y+10={120}^{\circ }\\ y={110}^{\circ }\end{array}$

Therefore, the length of $CD={110}^{\circ }$ .

b.

To determine

To find: the angle of $ED$ .

Answer to Problem 20CR

  $ED={70}^{\circ }$ .

Explanation of Solution

Given:

  

Calculation:

According to the question, there is a circle in which $PT=4,TQ=16,PS=5$ .

The objective is to find $ED$ .

From part (a), $y=CD={110}^{\circ }$ , therefore,

  $\begin{array}{l}z+y={180}^{\circ }\\ z+110={180}^{\circ }\\ z=180-110={70}^{\circ }\end{array}$

Therefore, the angle of $ED={70}^{\circ }$ .