Question

Given: AC and AE are common external tangents of G and D. BC= 123 GB=20 and AG=101. What is the measure of AC?​

Answer 1

The length of AC is 222 units.

Explanation:

Given AC and AE are common external tangents of G and D.

BC= 123 , GB=20 and AG=101.

We have to find the measure of AC.

As, a straight line joined from the center i.e radius is perpendicular to tangent drawn. Therefore,

In ΔABG, by Pythagoras theorem

`AG^2=AB^2+BG^2`

⇒
`101^2=AB^2+20^2`

⇒
`AB^2=10201-400=9801`

⇒ AB=99 units.

Hence, AC=AB+BC=99+123=222 units.

The length of AC is 222 units.