Chord (Geometry)

A chord is a straight line segment whose endpoints both lie on a curve, most commonly a Circle. In Geometry, chords are fundamental objects that bridge points on circular arcs and reveal deep relationships between distance, angle, and area.

The most familiar chord is a Diameter, which passes through the center and represents the longest possible chord. Any other chord falls strictly inside the circle. The perpendicular distance from the center to a chord determines its length—a principle exploited in Engineering and Architecture when designing arches and domes.

Chords connect intimately to Calculus: the rate of change along a chord approximates instantaneous rates, foundational to Isaac Newton's method of tangents. They also govern central angles, which measure the arc they subtend and unlock formulas for Area and Circumference.

Historically, chord tables—precursors to modern trigonometric functions—enabled ancient astronomers and navigators to solve celestial problems. Today, chords appear wherever curves matter: in optics, acoustics, and orbital mechanics.

The beauty of a chord lies in its simplicity: two points, one line, infinite geometry waiting to unfold.

Related

Circle, Arc, Secant line, Tangent line, Central angle, Trigonometry