Chapter 10.4, Problem 9PSA

To determine

To Prove : $\overline{WX}\cong \overline{YZ}$

Answer to Problem 9PSA

1

Explanation of Solution

Given information : $\begin{array}{l}\overline{PW}\text{ and }\overline{PZ}\text{ are common tangents to the circle with centre A and B}\\ \text{at W, X, Y and Z}\text{.}\end{array}$

  

As the lengths of tangents drawn from an external point to a circle are equal.

  $\begin{array}{l}\text{Therefore, }\overline{PW}\cong \overline{PZ}\\ \text{And}\overline{PX}\cong \overline{PY}\mathrm{...........}(1)\\ \text{As }PW=PX+WX\text{ and }PV+YZ=PZ\\ \text{So, }PX+WX\cong PY+YZ\mathrm{......}(2)\\ \text{From (1) and (2), we get}\\ \overline{WX}\cong \overline{YZ}\end{array}$