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 \(JED \)?

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