[1F.2] Let A, B, C, and D be placed consecutively on a circle. Let W, X, Y, and Z be the midpoints of AB, BC, CD, and DA, respectively. Show that chords WY and XZ are perpendicular. [1F.5] In AABC, prove that ZA is a right angle if and only if the length of the median from A to BC is exactly half the length of side BC. [1F.9] Let O be the center of the circumcircle of AABC, and extend the bisector of ZA so that it meets the circle at point P. Prove that the radius OP is perpendicular to BC