Chapter 10, Problem 5RP

To determine

To find : The Length of $\stackrel{⌢}{WX}$

Answer to Problem 5RP

  $\stackrel{⌢}{WX}=125°$

Explanation of Solution

Given information :

PZ and PY are tangent to inner circle. $\stackrel{⌢}{YZ}=110°$

  

Formula Used:

The angle subtend by an arc of a circle at its twice of the angle it subtends anywhere on the circumference.

Calculation :

  $YZ=110°,\angle YOZ=110°$

Now, $\angle YPZ=\frac{1}{2}\times \angle YOZ=55°$

In quadrilateral, CPDT, we get

  $\begin{array}{l}\angle WPX+\angle PXO+\angle XOW+\angle OWP=360°\\ \Rightarrow \angle XOW=360°-(90+90+55°)\\ \Rightarrow \angle XOW=125°\\ \Rightarrow WX=125°\end{array}$