The Butterfly Theorem. Suppose M is the midpoint of a chord P Qof a circle and AB and CD are two other chords that pass through M.Let AD and BC intersect P Q at X and Y , respectively. Then M isalso the midpoint of XY .
1. Prove the Butterfly Theorem. [10]
Hint: You know a lot about angles in a circle, and abouttriangles, and cross ratios, and all sorts of things . . .
