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a / b = √ ( R / ( R + R₁ ) )

Angle CFE = 90°

Angle ABE = 15°

Missing Angle ACS = 45°

Mathematical Proof

Parametric & Cartesian Circle Graphs

Intersection between 2 lines

Angle BDC = 132°

OP / BP = 1.09907101153

Ratio of AB / AD = 1 : 1

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Isosceles Triangle

tan X = 26.9883285248

Yellow = 0.134753021113

X = FEG = 10

Yellow = 15 Square Units

Red : Green : Blue = 4 : 5 : 3

Triangle ABC Perimeter = 50

cos GEH = 0.25 = 1 / 4

tan CED = 1 / 2 = 0.5

NEW: R = 5.03322295685

Radius R = 5.03322295685

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Elaborated: BE = 1.61803398875

BE = 1.61803398875

Fraction = 2.2360679775

w = l sin 45 ⇒ Red : Blue = 1

X = 9

AB Squared = 250

X + Y = 10.0902485737

X = 3

Shaded Fraction = 3 / 5 = 0.6

X = 2.2360679775 = √ 5

X = 7

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X = ACB = 22.5°

Square Root Five

Length of Red Segment = 3

Line Segment CE = 5

Blue Area = 16.8337520964

Proof that R = R₁ ⋅ √ 2

Radius R = 5

Simplified: Radius R = 5

AC = 15.0996688705

Ratio of Blue : Yellow = 7

Blue Fraction = 5 / 11

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Blue Area = 26 Square Units

Red : Green = Blue : Yellow

𝛼 = 30 Square Units

Segment AB = 12

Ratio of Red : Green = 1 / 2

X = BCD = 15°

Ratio of Green / Magenta = 1

X = DH = 3

Simplified: Blue Area = 13 Square Units

Blue Area = 13 Square Units

Mathematical Proof