Geometry Problem 182: Intersecting, Overlapping Circles, Find an angle, Auxiliary Lines.

In the figure below, A and B are the centers of the overlapping circles. EF is tangent at B. If line AE and circle A meet at G, find the measure of angle AGD. View or post a solution

Overlapping circles, find an angle

Tangent line appears,
Circles meet and overlap,
Auxiliary lines guide.

Problem 182 on Twitter:

What is the measure of the angle we see at the end of this animation? How can we formally prove this true? (Source: @gogeometry). https://t.co/89d1Gn9qat @geogebra #MTBoS #ITeachMath #math #maths #EdTech #geometry #proof #MathEd #MathEdTech pic.twitter.com/4Sf2JsjANV
— Tim Brzezinski (@Brzezinski_Math) November 2, 2019