Geometry Intermediate

Inscribed Angle Theorem

The inscribed angle is always half the central angle (and half the intercepted arc). Give any one of the three and find the others — with a color-coded diagram.

3 input modes
Inscribed = ½ central
Color-coded diagram
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Step-by-Step Solution
Inscribed Angle Diagram
The Inscribed Angle Theorem
Inscribed angle = ½ × intercepted arc Inscribed angle = ½ × central angle Central angle = intercepted arc (in degrees)
Special Case: Semicircle

When the intercepted arc is a semicircle (180°), the inscribed angle is always exactly 90°. Any angle inscribed in a semicircle is a right angle.

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