The way central and inscribed angles work in a circle is really interesting and helpful in geometry!

Central Angle:

• A central angle is made by two lines (called radii) that go from the center of the circle to the edge.
• For example, if angle $AOB$ is a central angle, it measures the same as the part of the circle (arc) between points A and B, called arc $AB$.

Inscribed Angle:

• An inscribed angle, like angle $APB$, is created where two lines (called chords) meet on the edge of the circle.
• Here’s the cool part: the inscribed angle is always half the size of the central angle that covers the same arc. So, for the inscribed angle $APB$, its size will be $\frac{1}{2} \times \text{m}(\angle AOB)$.

This idea is really useful for solving problems about circles. Just keep this in mind: inscribed angles are always half the size of their matching central angles!