Chapter 10, Problem 20RP

To determine

To find : $\text{m}\overrightarrow{AB}$ and $\text{m}\overrightarrow{CD}$ of a circle.

Answer to Problem 20RP

  $\text{m}\overrightarrow{AB}=110°$ and $\text{m}\overrightarrow{CD}=50°$

Explanation of Solution

Given information :

We know that, $\text{m}\overrightarrow{AO}+\text{m}\overrightarrow{BC}=200,\text{m}\angle P=30°$

  

Formula Used:

The angle made by the two secants intersecting outside a circle is half the difference between intercepted arc measures.

Calculation :

Since, $\text{m}\stackrel{⌢}{AO}+\text{m}\stackrel{⌢}{BC}=200°$

  $\therefore \text{m}\stackrel{⌢}{AB}+\text{m}\stackrel{⌢}{CD}=160°\mathrm{...}(1)$

Also, $\text{m}\stackrel{⌢}{AB}-\text{m}\stackrel{⌢}{CD}=30°\times 2=60°\mathrm{...}(2)$

Solving (1) and (2), we get

  $\begin{array}{l}\text{m}\stackrel{⌢}{AB}=110°\\ \text{m}\stackrel{⌢}{CD}=50°\end{array}$