IT-CESENATICO 2016 Problem 3

Let $\Gamma$ be the excircle of triangle $ABC$ opposite to the vertex $A$ (namely, the circle tangent to $BC$ and to the prolongations of the sides $AB$ and $AC$ from the part $B$ and $C$ ). Let $D$ be the center of $\Gamma$ and $E$ , $F$ , respectively, the points in which $\Gamma$ touches the prolongations of $AB$ and $AC$ . Let $J$ be the intersection between the segments $BD$ and $EF$ .

Prove that $\angle CJB$ is a right angle.