Question

Angle C is inscribed in circle O. AB is a diameter of circle O. What is the radius of circle O?

Answer 1

6.5 units

Explanation:

In circle with center O, AB is diameter.

`\therefore m\angle ACB = 90°\\`

(Angle inscribed in a semicircle)

`\therefore \: in\: \triangle ABC, \:AB \: is\: hypotenuse \\`

By Pythagorean theorem:

`AB = \sqrt{ {12}^(2) + {5}^(2) } \\ = √(144 + 25) \\ = √(169) \\ AB \: = 13 \\ r = (13)/(2) = 6.5 \: units`