Question

Circle O has a diameter of length 16. A point C is located outside of the circle such that it lies 12 units from the circle's center. What would the length of a segment drawn from C tangent to circle O be? Express your answer in simplest radical form.

Answer 1

The Length of a segment drawn from C tangent to circle O is

AC = x = 9 units

Explanation:

Given data

From the Δ OAC

Radius of circle OA = 8 units

OC = 12 units

AC = Length of a segment drawn from C tangent to circle O = x

We know that in Δ OAC

`OC^(2) = OA^(2) + AC^(2)`

`12^(2) = 8^(2) + x^(2)`

`x^(2) = 144 - 64`

`x^(2) = 80`

x = 8.9 units ≈ 9 units

Therefore Length of a segment drawn from C tangent to circle O is

AC = x = 9 units