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

Answer:

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

AC = x = 9 units

Step-by-step 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