A coffee break geometry problem 2

Geometry Level pending

This time the tables are turned, instead of triangles cut out of a circle, there is a circle cut out of a isosceles triangle! Again you must find the area of the shaded region.

You are given that the angle formed by FCB is 29.74 degrees, the angle CBF is 23.39 degrees, and the angle CGB is 90 degrees. The length of CB is 8.06

The length of the line segments AB, CF, FG, and FB are each whole numbers.

*Edit added for clarification: AF is a whole number, and CFG is a straight line.


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