Question

A, B, and C are points on the circumference of a circle, centre O. Angle ABC = 43 degrees. (a) Find the size of the angle AOC

Answer 1

The size of angle AOC can be determined by using the property that angles in the same segment are equal. Since both angle ABC and angle AOC are subtending the same arc AC, they are equal. Therefore, the size of angle AOC is 43 degrees.

Answer 2

To find the size of angle AOC, we can use the property that the angle subtended by an arc at the center of a circle is twice the angle subtended by the same arc at any point on the circumference.

Since angle ABC is given as 43 degrees, it is the angle subtended by arc AC at point B. Therefore, angle AOC will be twice angle ABC.

Angle AOC = 2 * angle ABC = 2 * 43 degrees = 86 degrees.

Hence, the size of angle AOC is 86 degrees.