Question

Given: AC is a diameter of circle O and the measure of angle BAC =27. Find the

measure of angle BOC.

Answer 1

`m\angle BOC=54^\circ`

Explanation:

First, we establish the following:

• B, A and C are on the circle
• AC is a diameter
• The center of the circle is O

Therefore:

`\angle BAC$ is the angle subtended by arc BC on the circumference.\\\angle BOC$ is the angle subtended by arc BC at the centre.`

The inscribed angle theorem states that an angle inscribed in a circle is half of the central angle that subtends the same arc on the circle.

Therefore:

`\angle BOC =2\angle BAC\\\angle BOC=2 * 27\\m\angle BOC=54^\circ`