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B, F, I & Q are not Collinear Points

X = 2.44948974278

Mathematical Proof without Words

X = AC = 4.24264068712

Square ABCD Area = 16

Shaded Area = 24.6458333333

Quadrilateral ABCD Area = 2

Radius R = AO = BO = 20

Trapezoid ABCD Area = 12

XY = 8.0622577483