Let ABC be an acute scalene triangle such that AB<AC. The midpoints of sides AB and AC are M and N, respectively. Let P and Q be points on the line MN such that ∠CBP=∠ACB and ∠QCB=∠CBA. The circumscribed circle of triangle ABP intersects line AC at D (D=A) and the circumscribed circle of triangle AQC intersects line AB at E (E=A). Show that lines BC,DP, and EQ are concurrent.Nicolás De la Hoz, Colombia geometryconcurrencyconcurrent