RU-SPB 2018 Problem 93

$ABC$ is acuteangled triangle. Variable point $X$ lies on segment $AC$ , and variable point $Y$ lies on the ray $BC$ but not segment $BC$ , such that $\angle ABX+\angle CXY =90$ . $T$ is projection of $B$ on the $XY$ . Prove that all points $T$ lies on the line.