Question 160
Let $ABC$ be a triangle that is not isosceles at $A$, and $\Gamma$ its circumcircle. Let $N$ be the midpoint of the arc of $\Gamma$ between $B$ and $C$ that contains $A$. Let $I$ be the incentre of $ABC$, $J$ the centre of the $A$-excircle of $ABC$, and $K$ the intersection point of $BC$ with the external bisector of $\angle BAC$.
Show that $(JN) \perp (IK)$.
Show that $(JN) \perp (IK)$.