# The length of the radius of two circles are 5 cm and 3 cm. The distance between their center is 13 cm. Find the length of the tangent who touches both the circles?

##### 1 Answer
Feb 2, 2017

$\sqrt{165}$

#### Explanation:

Given :
radius of circle A = 5 cm,
radius of circle B = 3cm,
distance between the centers of the two circles = 13 cm.

Let ${O}_{1} \mathmr{and} {O}_{2}$ be the center of Circle A and Circle B, respectively, as shown in the diagram.

Length of common tangent $X Y$,
Construct line segment $Z {O}_{2}$, which is parallel to $X Y$
By Pythagorean theorem, we know that
$Z {O}_{2} = \sqrt{{O}_{1} {O}_{2}^{2} - {O}_{1} {Z}^{2}} = \sqrt{{13}^{2} - {2}^{2}} = \sqrt{165} = 12.85$

Hence, length of common tangent $X Y = Z {O}_{2} = \sqrt{165} = 12.85$ (2dp)