Question

What is the length of the radius of circle A?

Answer 1

Given:

CD = 18 cm

CE = 8 cm

To find:

The length of the radius of the circle A.

Solution:

Let the radius of the circle be x.

AD = AE = x

CA = CE + AE

CA = 8 + x

The angle between a tangent and radius is always right angle.

Therefore triangle ADC is a right triangle.

Using Pythagoras theorem:

`AD^2+CD^2=CA^2`

`x^2+18^2=(8+x)^2`

Using algebraic identity:
`(a+b)^2=a^2+2ab+b^2`

`x^2+324=8^2+16x+x^2`

`x^2+324=64+16x+x^2`

Subtract x² from both sides.

`324=64+16x`

Subtract 64 from both sides.

`260=16x`

Divide by 16 on both sides, we get

`16.25=x`

The length of the radius of the circle is 16.25 cm.