Triangle from Perpindiculars

Geometry Level 3

Triangle ABCABC has AB=AC AB=AC . DD is the foot of the perpendicular from AA to BCBC. EE is the foot of the perpendicular from BB to ACAC. ADAD and BEBE intersect at HH, the orthocenter of triangle ABCABC. Let JJ be the midpoint of AHAH. What is the measure (in degrees) of JEDJED ?

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