Question 118
Let $ABC$ be a triangle and let $J$ be the centre of its $A$-excircle. Let $K$ be the reflection of the point $J$ across the segment $[BC]$. Let $E$ and $F$ be the points on the lines $(BJ)$ and $(CJ)$ such that $\widehat{EAB} = \widehat{CAF} = 90^{\circ}$. Show that $\widehat{FKE} + \widehat{FJE} = 180^{\circ}$.