Question

which of the following is circle o with a central angle and a corresponding inscribed angle? show hints

Explanation:

Step1: Recall definitions

A central - angle has its vertex at the center of the circle, and an inscribed - angle has its vertex on the circle.

Step2: Analyze each option

In the first option, $\angle BOC$ is a central angle (vertex at $O$, the center of the circle) and $\angle BAC$ is an inscribed angle (vertex $A$ on the circle). In the second option, the point marked as $O$ is not the center of the circle for the angles shown. In the third option, there is no central angle shown. In the fourth option, the angles do not meet the criteria of a central - angle and a corresponding inscribed - angle.

Answer:

The first option (the circle with $\angle BOC$ as the central angle and $\angle BAC$ as the inscribed angle)