Problem

Source: Moldova TST 2018

Tags: geometry



Let $\Omega $ be the circumcincle of the quadrilateral $ABCD $ , and $E $ the intersection point of the diagonals $AC $ and $BD $ . A line passing through $E $ intersects $AB $ and $BC$ in points $P $ and $Q $ . A circle ,that is passing through point $D $ , is tangent to the line $PQ $ in point $E $ and intersects $\Omega$ in point $R $ , different from $D $ . Prove that the points $B,P,Q,$ and $R $ are concyclic .