Question

AC is tangent to circle o at point c. What is the length of AC? ___________ units. diagram below pls help

Answer 1

AC = 4 units

Explanation:

`OB = OC = 3 (Radii \:of \:same \:circle) \\</p><p>OA = OB + AB = 3 + 2 = 5\\</p><p>OA \perp AC.. (tangent\: \perp radius) \\</p><p>\therefore m\angle OCA = 90\degree \\`

By Pythagorean theorem:

`AC^2 = OA^2 - OC^2 \\</p><p>= 5^2 - 3^2 \\</p><p>= 25-9\\</p><p>= 16\\</p><p>AC =\pm √(16)\\</p><p>AC = \pm 4`

Since, side of a triangle can't be negative.

Therefore, AC = 4 units