Katana VentraIP

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.

Equivalently, an inscribed angle is defined by two chords of the circle sharing an endpoint.


The inscribed angle theorem relates the measure of an inscribed angle to that of the central angle subtending the same arc.


The inscribed angle theorem appears as Proposition 20 on Book 3 of Euclid's Elements.

Ellipse

Hyperbola

Parabola

Inscribed angle theorems exist for ellipses, hyperbolas and parabolas, too. The essential differences are the measurements of an angle. (An angle is considered a pair of intersecting lines.)

(1990). Excursions in Geometry. Dover. pp. 17–23. ISBN 0-486-26530-7.

Ogilvy, C. S.

Gellert W, Küstner H, Hellwich M, Kästner H (1977). The VNR Concise Encyclopedia of Mathematics. New York: Van Nostrand Reinhold. p. 172.  0-442-22646-2.

ISBN

(1974). Elementary Geometry from an Advanced Standpoint (2nd ed.). Reading: Addison-Wesley. pp. 192–197. ISBN 0-201-04793-4.

Moise, Edwin E.

"Inscribed Angle". MathWorld.

Weisstein, Eric W.

Relationship Between Central Angle and Inscribed Angle

at cut-the-knot

Munching on Inscribed Angles

With interactive animation

Arc Central Angle

With interactive animation

Arc Peripheral (inscribed) Angle

With interactive animation

Arc Central Angle Theorem

At bookofproofs.github.io