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

$\text{4cm}$

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B

$\text{6cm}$

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C

$\text{8cm}$

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D

$\text{12cm}$

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Solution

## The correct option is C $\text{8cm}$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, $\text{CD=AD=4cm}$.$\text{CD=BD=4cm}$Therefore,$\begin{array}{rcl}& & \text{AB=AD+BD}\\ & & \text{=4+4}\\ & & \text{=8cm}\end{array}$Hence, option C is the correct answer.

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