Problem 458: Square, Semicircle, Circular Sector, Internal Common Tangent, Measurement

The figure shows a square ABCD of side a. The semicircle of diameter AB and the circular sector of center D are tangent at E. If FG is the internal common tangent, prove that .
 

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Proposed Problem 459.
Right triangle, Squares, Distance, Measurement.

Proposed Problem 457.
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Proposed Problem 456.
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Proposed Problem 455.
Rhombus, Inscribed Circle, Angle, Chord, 45 Degrees.