1F.2] Let A, B, C, and D be placed consecutively on a circle. Let W , X, Y , and Z be the midpoints of dAB, dBC, dCD, and dDA, respectively. Show that chords W Y and XZ are perpendicular. [1F.5] In ABC, prove that A 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 ABC, and extend the bisector of A so that it meets the circle at point P . Prove that the radius OP is perpendicular to BC