Let $\vartriangle ABC$ be a scalene (i.e. non-isosceles) triangle with circumcentre $O$. Let $J_A$, $J_B$, $J_C$ be the $A$-, $B$-, $C$-excentre of $\vartriangle ABC$ respectively. $OJ_A$ intersects $BC$ at $X$, $OJ_B$ intersects $CA$ at $Y$ , $OJ_C$ intersects $AB$ at $Z$. Prove that $AX$, $BY$ , $CZ$ and the Euler line of $\vartriangle ABC$ are concurrent. Note: The $A$-excentre of $\vartriangle ABC$ is the centre of the circle that is tangent to the line segment $BC$, to the ray $AB$ beyond $B$, and to the ray $AC$ beyond C. The $B$-, $C$-excentre of $\vartriangle ABC$ are defined similarly. The Euler line of a triangle is the line which passes through the orthocentre and the circumcentre of the triangle.