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X = BDC = 25

 

X = BF = 1.25 = 5 / 4

Proof that k = 1.61803398875

X = BFC = 135

Angle ABC = 30

Quarter Circle Radius R = 5

Green Area = 360.642013806

Radius R = 3.48316324759

Max ( a / b ) = 1.61803398875

Semicircle Area = 1.57079632679