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:
“[One cannot express lack of knowledge in affirmative language.] This idea is more firmly grasped in the form of interrogation: “What do I know?”Mthe words I bear as a motto, inscribed over a pair of scales.”
—Michel de Montaigne (1533–1592)
“The inhabitants of earth behold commonly but the dark and shadowy under side of heaven’s pavement; it is only when seen at a favorable angle in the horizon, morning or evening, that some faint streaks of the rich lining of the clouds are revealed.”
—Henry David Thoreau (1817–1862)