TH-TMO 2020 Problem 4

Let $\triangle ABC$ be a triangle with altitudes $AD,BE,CF$ . Let the lines $AD$ and $EF$ meet at $P$ , let the tangent to the circumcircle of $\triangle ADC$ at $D$ meet the line $AB$ at $X$ , and let the tangent to the circumcircle of $\triangle ADB$ at $D$ meet the line $AC$ at $Y$ . Prove that the line $XY$ passes through the midpoint of $DP$ .