6th Junior Balkan Mathematical Olympiad Problems 2002

1.  The triangle ABC has CA = CB. P is a point on the circumcircle between A and B (and on the opposite side of the line AB to C). D is the foot of the perpendicular from C to PB. Show that PA + PB = 2·PD. 2.  The circles center O1 and O2 meet at A and B with the centers on opposite sides of AB. The lines BO1 and BO2 meet their respective circles