Question

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

Answer 1

Answer:

$m\angle BOC=54^\circ$

Step-by-step 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:

$\angle BOC =2\angle BAC\\\angle BOC=2 \times 27\\m\angle BOC=54^\circ$