### GMAT Prep - Math - Geometry - Central and Inscribed Angles by Knewton

Go to http://www.knewton.com/gmat/ for hundreds of GMAT math and verbal concepts, thousands of practice problems and much more. Knewton GMAT is a GMAT prep course that redefines everything you thought you knew about online learning. Central angles and inscribed angles are two sorts of angles we talk about that relate to circles. Notice that the central angle is in the middle of the circle. Its vertex is the middle of the circle. An inscribed angle, on the other hand, has one endpoint on the edge of the circle and then cuts across the rest of the circle. The vertex of its angle is on the circumference. Here are some interesting points about inscribed angles. All three of these inscribed angles have the same endpoints; they end at the same place on the circle. Their vertices, however, are on three different spots. Nonetheless, any inscribed angle that ends on the same two points has the same measure unless the vertex is on the minor arc. As you can see here, the circle on the left and on the right have the same endpoints, but they have a vertex on opposite arcs and are, as a result, supplementary. Another interesting property of inscribed angles is that any inscribed angle whose endpoints are a diameter is a right angle, or 90 degree angle. The Central Angle Theorem relates angles with the same endpoints and says that an inscribed angle and a central angle, when they have the same endpoints on the edge of the circle have this relationship: the inscribed angle is half the measure of the central angle. In this example we can see that the purple inscribed angle and the black central angle share the same endpoints. If the inscribed angle measure x, the central angle will measure 2x. For example, if the central angle is 90 degrees, the inscribed angle is 45 degrees. Subscribe to this channel for tips, explanations, and Q&A about the GMAT and getting your MBA.

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