Question

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?

Answer 1

`sqrt165`

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 and O_2` be the center of Circle A and Circle B, respectively, as shown in the diagram.

Length of common tangent `XY`,
Construct line segment `ZO_2`, which is parallel to `XY`
By Pythagorean theorem, we know that
`ZO_2=sqrt(O_1O_2^2-O_1Z^2)=sqrt(13^2-2^2)=sqrt165=12.85`

Hence, length of common tangent `XY=ZO_2=sqrt165=12.85` (2dp)