Problem 455: Rhombus, Inscribed Circle, Angle, Chord, 45 Degrees
The figure shows a rhombus ABCD with
the inscribed circle O. Points E, F, and G are the tangency
points. Circle O intersects OB and OC at H and J, respectively.
If chords EJ and GH meet at K, prove that the measure of angle
JKG is 45 degrees.