Question

make a conjecture. let points a and b stay in the same position. what would happen to the angle formed if the vertex of angle aob was moved from the center to point c, which lies on the circle? the measure of angle acb is dropdown the measure of angle aob.

Explanation:

Step1: Recall circle - angle theorem

The measure of an inscribed - angle (angle with vertex on the circle) is half of the measure of the central - angle (angle with vertex at the center of the circle) that subtends the same arc.

Step2: Identify the angles

Angle $\angle AOB$ is a central angle and angle $\angle ACB$ is an inscribed angle, and they subtend the same arc $\overset{\frown}{AB}$.

Answer:

half of