CN-TST 2017 Problem 20

In $\varDelta{ABC}$ ,the excircle of $A$ is tangent to segment $BC$ ,line $AB$ and $AC$ at $E,D,F$ respectively. $EZ$ is the diameter of the circle. $B_1$ and $C_1$ are on $DF$ , and $BB_1\perp{BC}$ , $CC_1\perp{BC}$ .Line $ZB_1,ZC_1$ intersect $BC$ at $X,Y$ respectively.Line $EZ$ and line $DF$ intersect at $H$ , $ZK$ is perpendicular to $FD$ at $K$ .If $H$ is the orthocenter of $\varDelta{XYZ}$ ,prove that: $H,K,X,Y$ are concyclic.