Given the figure below, the theorem states, "if AB and BC make up a broken chord in a circle, where BC > AB, and if M is the midpoint of arc ABC, then the foot F of the perpendicular from M on BC is the midpoint of the broken chord ABC.
Use GSP to find the measure of AB, BF and FC. Notice that the sumof AB and BC is equal to FC. Thereore, F is the midpoint of the broken chord.