Inscribed Semicircle Riddle
Geometry
Level
2
As shown in the diagram, triangle \(ABC\) inscribes a semi-circle such that \(AB\) and \(AC\) are tangents at points \(D\) and \(E,\) respectively.
\(GH\) is the diameter of the semi-circle, and point \(F\) is the intersection of \(DH\) and \(EG.\)
If the 2 angles highlighted in blue are equal, find that angle in degrees.
\(\)
Note: The diagram is not drawn to scale.
by
Worranat Pakornrat