Question 13
Let $ABCD$ be a convex quadrilateral such that $AB^2 + BC^2 = AD^2 + CD^2$. Points $X$ and $Y$ are chosen such that $XD \perp CD$, $XB \perp AB$, $YB \perp BC$ and $YD \perp AD$. Let lines $AC$ and $XY$ meet at $T$ and $M$ be the midpoint of segment $XY$. Prove that points $T, M, B, D$ lie on a circle.