Inscribed angle

In geometry, an inscribed angle is the angle formed in the interior of a circle when two chords intersect on the circle. It can also be defined as the angle subtended at a point on the circle by two given points on the circle.

In Euclidean geometry, the inscribed angle theorem (Proposition 20 in Book 3 of Euclid's Elements) relates the measure of an inscribed angle to that of the central angle intercepting the same arc.

Note that this theorem is not to be confused with the angle bisector theorem, which also involves angle bisection (but of an angle of a triangle not inscribed in a circle).

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