Let D be a point inside an acute triangle ABC, such that ∠BAD=∠DBC and ∠DAC=∠BCD. Let P be a point on the circumcircle of the triangle ADB. Suppose P are itself outside the triangle ABC. A line through P intersects the ray BA in X and ray CA in Y, so that ∠XPB=∠PDB. Show that BY and CX intersect on AD. geometryconcurrentequal angles