About Circle Chords
What Is a Chord?
A chord is a straight line segment whose endpoints lie on the circumference of a circle. The diameter is the longest possible chord, passing through the center. Every chord divides a circle into two regions: a smaller segment and a larger segment.
Chord Length Formula
Given the radius r and the central angle theta (in radians), the chord length is c = 2r x sin(theta/2). Alternatively, if you know the perpendicular distance d from the center to the chord, then c = 2 x sqrt(r² - d²).
Related Properties
Each chord defines several related measurements: the arc it subtends, the central angle, the segment area (between chord and arc), and the segment height (distance from chord midpoint to arc). These are all interconnected through the radius.
Applications
Chord calculations are used in structural engineering (arch design), manufacturing (circular cuts), navigation (great circle routes), optics (lens design), and music theory (string vibration patterns). Understanding chord properties is fundamental in circular geometry.