The Inscribed Angle Theorem

Introduction

An inscribed angle is formed when two secant lines intersect on a circle. It can also be formed using a secant line and a tangent line intersecting on a circle. A central angle, on the other hand, is an angle whose vertex is the center of the circle and whose sides pass through a pair of points on the circle, therefore subtending an arc. In this post, we explore the relationship between inscribed angles and central angles having the same subtended arc. The angle of the subtended arc is the same as the measure of the central angle (by definition).

inscribed-angle-theorem

In the first circle, $latex \angle O$ is a central angle subtended by arc $latex AB$. Angle $latex Q$ is an inscribed angle subtended by arc $latex PR$. In the second circle, $latex \angle T$ is an inscribed angle and $latex \angle V$ is a central angle. Both angles are subtending arc $latex SU$. Continue reading