IR-MO 2004 Problem 11

assume that ABC is acute traingle and AA' is median we extend it until it meets circumcircle at A". let $AP_a$ be a diameter of the circumcircle. the pependicular from A' to $AP_a$ meets the tangent to circumcircle at A" in the point $X_a$ ; we define $X_b,X_c$ similary . prove that $X_a,X_b,X_c$ are one a line.