Question

Circle A has radius 5, and Circle B has radius 2. If CD = 12 and is a common

tangent, what is AB?

Answer 1

`3√(17)$ or \approx 12.37$ Units`

Explanation:

In the attached diagram

CA=CO+OA

CO=DB

Therefore:

5=2+OA

OA=3 Units

The angle between a tangent line and a radius is 90 degrees. therefore triangle OAB is a right triangle with:

OB=12 units

OA=3 units

Using Pythagoras theorem

`AB=√(3^2+12^2)\\ =√(153)\\=3√(17)$ or \approx 12.37$ Units`