An interactive demonstration of the "intersection of chords of an angle" theorem known since before Archimedes.
The theorem as taken from Heath is "if two chords drawn in fixed directions between two lines forming an angle intersect in a point the ratio of the rectangles under the segments is independent of the position of the point."
Point of intersection of the chords can be changed by dragging points F or C. The direction of the chords can be
changed using the small circular handles attached to points F and C.
When point F is positioned at point A, FL = EL = AK, BL = BK and CL = CK from which it is easy to derive the formula involving AK, BK and CK.
The initial configuration illustrates the instance where the two chords are anti-parallel to the central axis of the angle at A.