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By Freya Edholm
As you may know, the measure of an inscribed angle is half the measure of the arc. A diameter crosses a arc, so what is the measure of the inscribed angle on the diameter? Yup, it is . So, it's simply a right angle!
Preparing for a math contest?
Working through past problems on one idea at a time is one of the most effective ways to prepare. These are real problems from the AMC 8 and AMC 12, the national math competitions for middle and high school students, each with a worked solution on LIVE by Po-Shen Loh.
- Inscribed angle problems 18 from AMC 8, AMC 12
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Read Lockhart's Lament, pages 20 to 22. It gives a charming nonstandard proof of the fact that inscribed angles on a diameter are right angles.
(The whole article is really good too, if you have time! :)