Question

AB and CD are two common tangents to circles which touch each other at C. If D lies on AB such that $ \text{CD=4 cm}$, then AB is equal to

• A. $\text{4 cm}$
• B. $\text{6 cm}$
• C. $\text{8 cm}$
• D. $\text{12 cm}$

Answer 1

The correct option is C

$\text{8 cm}$

Explanation for the correct option:

We know that lengths of tangents drawn from an exterior point are equal.

Hence,from the figure,we get,

D is the external point,

Therefore, $\text{CD=AD=4 cm}$.

$\text{CD=BD=4 cm}$

Therefore,

$\begin{array}{rcl}& & \text{AB=AD+BD}\\ & & \text{= 4 + 4}\\ & & \text{= 8 cm}\end{array}$

Hence, option C is the correct answer.