Inscribed Angle Calculator
Calculate an inscribed angle, intercepted arc, or related central angle using the inscribed angle theorem with clear steps. This page is written for students who need both a fast answer and a clear explanation of the method, so it includes the formula, steps, examples, common mistakes, and practical notes.
The inscribed angle theorem in plain language
An inscribed angle sits on the circle, and its sides intercept an arc. The key theorem says that an inscribed angle measures half of its intercepted arc. The Khan Academy proof of the inscribed angle theorem gives a proof-based explanation of this theorem, while this calculator focuses on the practical homework conversions students usually need.
Formula and example
A central angle and an inscribed angle are not the same thing. If both intercept the same arc, the central angle equals the arc measure, while the inscribed angle is half of it.
Common questions
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An inscribed angle is an angle whose vertex lies on a circle and whose sides are chords or secants of the circle. It intercepts an arc between the two points where its sides meet the circle.
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The inscribed angle theorem says that an inscribed angle is half the measure of its intercepted arc. If the intercepted arc is 100 degrees, the inscribed angle is 50 degrees.
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A central angle has its vertex at the center of the circle and usually has the same measure as its intercepted arc. An inscribed angle has its vertex on the circle and measures half of its intercepted arc.
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If an inscribed angle intercepts a semicircle, the intercepted arc is 180 degrees, so the inscribed angle is 90 degrees. This is a common right-triangle result in circle geometry.