Question

Geometry: Angles of Circles 1. Compare and contrast central angles and inscribed angles.
2. Explain how the two types of angles (above) are related if they share a common intercepted arc.

Accepted Answer

A central angle of a circle has its vertex at the center of the circle. The measure of a central angle is defined to be the measure of the intercepted arc.
An inscribed angle has its vertex on the circle (hence in (in or on)-scribed (drawn or written)). The measure of an inscribed angle is 1/2 the measure of the intercepted arc.
If a central angle and an inscribed angle intercept the same arc, the inscribed angle has measure 1/2 the central angle. (The proof requires 3 cases: if the 2 angles have a coincident side (the vertex for the central angle is on a side of the inscribed angle), if the vertex of the central angle is "inside" the inscribed angle, and if the vertex of the central angle is "outside" the inscribed angle.)

Math

Geometry: Angles of Circles 1. Compare and contrast central angles and inscribed angles. 2. Explain how the two types of angles (above) are related if they share a common intercepted arc.

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