SHARYGIN 2024 Problem 87

A convex quadrilateral $ABCD$ is given. A line $l \parallel AC$ meets the lines $AD$ , $BC$ , $AB$ , $CD$ at points $X$ , $Y$ , $Z$ , $T$ respectively. The circumcircles of triangles $XYB$ and $ZTB$ meet for the second time at point $R$ . Prove that $R$ lies on $BD$ .