In geometry, an inscribed angle is formed when two secant lines of a circle (or, in a degenerate case, when one secant line and one tangent line of that circle) intersect on the circle.
Typically, it is easiest to think of an inscribed angle as being defined by two chords of the circle sharing an endpoint.
The basic properties of inscribed angles are discussed in Book 3, Propositions 20-22 of Euclid's Elements. These are the inscribed angle is half the central angle, inscribed angles on the same arc of a chord are equal and the sum of the two distinct inscribed angles of a chord is 180°.
Famous quotes containing the words inscribed and/or angle:
“Farewell sadness
Good-day sadness
You are inscribed in the lines of the ceiling.”
—Paul Éluard (1895–1952)
“It is a mistake, to think the same thing affects both sight and touch. If the same angle or square, which is the object of touch, be also the object of vision, what should hinder the blind man, at first sight, from knowing it?”
—George Berkeley (1685–1753)