Proof: Inscribed Angle Theorem | Geometry

An angle inscribed in a circle has half the measure of a central angle cutting the same arc. This is a wonderful little result concerning inscribed angles, and we'll prove it in today's video geometry lesson! Our proof relies on the isosceles triangle theorem, which we proved in this lesson:    • Proof: Isosceles Triangle Theorem | G...  

We'll break the proof into three cases. Case 1 is where the center of the circle lies on a side of the angle, and thus the angle passes through the diameter. Case 2 is where the center of the circle lies in the interior of the angle. Case 3 is where the center of the circle lies in the exterior of the angle. Cases 2 and 3 will be easily proven by introducing a diameter and using case 1 from there!

Thanks to Nasser Alhouti, Robert Rennie, Barbara Sharrock, and Lyndon for their generous support on Patreon!

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I hope you find this video helpful, and be sure to ask any questions down in the comments!

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