On a line p which does not meet a circle K with center O, point P is taken such that OP⊥p. Let X=P be an arbitrary point on p. The tangents from X to K touch it at A and B. Denote by C and D the orthogonal projections of P on AX and BX respectively.
(a) Prove that the intersection point Y of AB and OP is independent of the location of X.
(b) Lines CD and OP meet at Z. Prove that Z is the midpoint of P. midpointFixed pointgeometry