Inscribed Semicircle Riddle

Geometry Level 2

As shown in the diagram, triangle ABCABC inscribes a semi-circle such that ABAB and ACAC are tangents at points DD and E,E, respectively.

GHGH is the diameter of the semi-circle, and point FF is the intersection of DHDH and EG.EG.

If the 2 angles highlighted in blue are equal, find that angle in degrees.


Note: The diagram is not drawn to scale.

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