Let ABC be a triangle such that AB < AC. Let the excircle opposite to A be tangent to the lines AB, AC and BC at points D, E and F, respectively, and let J be its centre. Let P be a point on the side BC. The circuracircles of the triangles BDP and CEP intersect for the second time at Q. Let R be the foot of the perpendicular from A to the line FJ. Prove that the points P, Q and R are collinear.

(The excircle of a triangle ABC opposite to A is the circle that is tangent to the line segment BC, to the ray AB beyond B, and to the ray AC beyond C.)