Question

The distance between the centres of two circles of radii 3 cm and 8 cm respectively is 13 cm. If PQ is the direct common tangent of the circles, then its length is

• A. $11$cm
• B. $12$ cm
• C. $13$ cm
• D. $14$ cm

Answer 1

Answer: (B)

$12$ cm

Consider the above figure, the radii of the first circle is $AP=3$ cm and the radii of the second circle is $QB=8$ cm.

Now since $AP=3$, therefore $QC=3$ and thus $BC=QB-QC=8-3=5$

We find the length $AC$ as follows:

$AC=\sqrt{{13}^2-5^2}=\sqrt{169-25}=\sqrt{144}=12$

Hence, $PQ=AC=12$ cm.