Chapter 9, Problem 11CR

To determine

To complete: the blank in the given statement.

Answer to Problem 11CR

  $\angle XPW\cong \angle YPW$

Explanation of Solution

Given information:

The given statement is “If arc lengths $XW\cong WY$ , then $\angle XPW\cong$

  $\underset{\_}{}$ ”

The given figure is as follows:

  

The lines $\overleftrightarrow{ZX}$ and $\overleftrightarrow{ZY}$ are tangent to circle.

Consider arc lengths $XW\cong WY$

And from figure, the radius is equal $XP\cong YP$

The two sectors $XPW\&\angle YPW$ are congruent. Since they are formed with equal radius

and arc lengths. So, they have same central angle.

Hence, $\angle XPW\cong \angle YPW$ .