In acute triangle ABCwith ∠BAC>∠BCA, let P be the point on side BC such that ∠PAB=∠BCA. The circumcircle of triangle APB meets side AC again at Q. Point D lies on segment AP such that ∠QDC=∠CAP.
Point E lies on line BD such that CE=CD. The circumcircle of triangle CQE meets segment CD again at F, and line QF meets side BC at G. Show that B,D,F, and G are concyclic geometryConcyclicequal anglescircumcircle