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circle in rectangle intersecting sides

Source: Slovenia 1998 3rd Grade P3

April 29, 2021
geometryrectangle

Problem Statement

A rectangle ABCDABCD with AB>ADAB>AD is given. The circle with center BB and radius ABAB intersects the line CDCD at EE and FF.
(a) Prove that the circumcircle of triangle EBFEBF is tangent to the circle with diameter ADAD. Denote the tangency point by GG. (b) Prove that the points D,G,D,G, and BB are collinear.
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