Question

The radii of $2$ circles are $7$ and $2$. If the distance between their centers is $13$, then the length of their common external tangent, is

• A. $10\sqrt{3}$
• B. $\frac{25}{2}$
• C. $12$
• D. $\frac{23}{2}$

Answer 1

Answer: (C)

$12$

The radii of the first circle is AP=2 cm and the radii of the second circle is QB=7 cm.

Now since AP=2, therefore QC=2 and thus BC=QB−QC=7−2=5

We find the length AC as follows:

$AC=\sqrt{{13}^2-5^2}$

$AC=12cm$

Hence, PQ=AC=12 cm.