The figure below shows a triangle ABC,
the perpendicular to AC at C and the perpendicular bisector of
BC meet at P_{1}, the perpendicular to AC at A and the
perpendicular bisector of AB meet at P_{2}, the tangent at B to circumcircle of triangle ABC meets AC extended at P_{3}. Prove that
points P_{2}, P_{1} and P_{3} are collinear.
