Triangle from Perpindiculars

Geometry Level 3

Triangle $ABC$ has $AB=AC$ . $D$ is the foot of the perpendicular from $A$ to $BC$ . $E$ is the foot of the perpendicular from $B$ to $AC$ . $AD$ and $BE$ intersect at $H$ , the orthocenter of triangle $ABC$ . Let $J$ be the midpoint of $AH$ . What is the measure (in degrees) of $JED$ ?