Quandaries and Queries


how do you find the length of a chord given the angle and radius of the circle



Let A be the midpoint of the chord PQ, C be the center of the circle and theta the angle subtended by the chord at the center of the circle. Triangle ACQ is a right triangle and hence

sin( theta/2) = |AQ|/r


chord length = 2 |AQ| = 2 r sin( theta/2)