Chapter 9.2, Problem 7WE

(a)

To determine

To Prove: The tangent AB is congruent to tangent CDis true or not.

Explanation of Solution

Given:

  

In the given figure, BZ and DZ are tangents.

If circle has a two tangent from a unique point then there are equal,

  $BZ=DZ$ and $AZ=CZ\mathrm{........}\left(1\right)$

The sum of BA and AZ is DZ

This implies that,

  $\begin{array}{l}BZ=DZ\hfill \\ BA+AZ=DC+CZ\hfill \end{array}$

It is known that $AZ=CZ$ from (1)

Subtract AZ from both sides to get,

  $BA=DC$

Therefore, it is proved that $AB\cong CD$ .

(b)

To determine

To state :The results in part (a) be true if the circles is congruent.

Explanation of Solution

Yes, the results in part (a) holds good if the circles are congruent.