Inscribed angle

In <a href="/facts/Geometry/wTQf5ffQ">geometry</a>, an inscribed angle is the <a href="/facts/Angle/gFUTEQYq">angle</a> formed in the interior of a <a href="/facts/Circle/9fy5ggKn">circle</a> when two <a href="/facts/Chord_(geometry)/aAyoEdLd">chords</a> intersect on the circle. It can also be defined as the angle <a href="/facts/Subtend/GQxln7lP">subtended</a> at a point on the circle by two given points on the circle.
Equivalently, an inscribed angle is defined by two chords of the circle sharing an endpoint.
The inscribed angle theorem relates the <a href="/facts/Angle/gFUTEQYq">measure</a> of an inscribed angle to that of the <a href="/facts/Central_angle/h00sYLNj">central angle</a> intercepting the same <a href="/facts/Circular_arc/RrehhCQR">arc</a>.
The inscribed angle theorem appears as Proposition 20 in Book 3 of <a href="/facts/Euclid%27s_Elements/nPKvCIxs">Euclid's Elements</a>.
Note that this theorem is not to be confused with the <a href="/facts/Angle_bisector_theorem/n7z1ARvB">Angle bisector theorem</a>, which also involves angle bisection (but of an angle of a triangle not inscribed in a circle).

Inscribed angle open-in-new

Inscribed angle