KnowraChordChordA chord is a line segment whose endpoints lie on a circle. A diameter is a chord that passes through the circle’s center.BriefConnectCircle: A plane curve whose points are all the same distance from a fixed center. A chord is defined by endpoints on this curve.Perpendicular bisector theorem for chords: A circle theorem stating that a radius perpendicular to a chord bisects the chord. It reduces chord-length calculations to a right triangle.Circular segment: A region of a circle bounded by a chord and the arc it subtends. Its area and height are calculated from the chord and arc.Secant line: A line that intersects a circle at two distinct points. Unlike a chord, it extends beyond the two intersection points.Radius: A line segment from a circle’s center to a point on the circle. Radii drawn to a chord’s endpoints form an isosceles triangle.Intersecting chords theorem: A theorem stating that products of segment lengths are equal when two chords intersect inside a circle. It links the parts of two crossing chords.Circular segment area: The area enclosed by a chord and its corresponding circular arc. It can be found by subtracting a triangle’s area from a sector’s area.Tangent line: A line that touches a circle at exactly one point. It meets the circle once, rather than joining two points on it.Central angle: An angle whose vertex is at the center of a circle and whose sides are radii. It determines the length of the chord between its endpoints.Inscribed angle theorem: A theorem stating that an inscribed angle measures half the central angle subtending the same arc. It relates a chord’s endpoints to angles on the circle.Show all 20Linked from 22 pagesPtolemy's theoremBroader topic: Every side and diagonal of the quadrilateral is a chord of its circumcircle.AlmagestRelated: Ptolemy’s chord table supplied the geometric calculations behind astronomical predictions.Butterfly theoremNarrower topic: The theorem is built from three chords arranged through one interior point.DiagonalCompared with: A chord need not connect vertices of a polygon, though polygon diagonals can be chords of a circumcircle.History of trigonometryBroader topic: Ancient Greek astronomers measured angles indirectly through the lengths of circle chords.Ancient Greek astronomyRelated: Chord tables gave astronomers a computational tool for translating angles into geometric lengths.Constant chord theoremNarrower topic: A chord is the geometric object whose length the theorem equates.Thales' theoremRelated: The two sides meeting at the semicircle's point are chords.Show all 22