Top 10.960

X = PQ = 3

Top 10.959

Angle ADB = 60

Top 10.958

Cos alpha = 3 / 5 = 0.6

X = BCE = 21

Orange Area = 8

X = CD = 6

X = Angle CBD = 10

Shaded Area = 13 / 18

Another Approach

New / Simplified

Green / Purple = 1.2 = 6 / 5

X = ABD = 24

Circle Area = 79.4142289853

Triangle Height BC = 6

Top 10.957

X = DE = 1.41421356237

Orange Area / Total Area = 80 / 169

[ Triangle ABC ] = 17.1865547358

X = AB = 11.313708499

Shaded Area = 18

ABD = 30 ( without Trigonometry )

[ ABC ] = Total Area = 50

[ CDOK ] = Shaded Area = 2

X = EF = 7.2

AHD = CHD = 45

Top 10.956

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

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Blue Quadrilateral Area = 2

X = DE = 3.87298334621

BMD = 17.1705468634

tan X = 0.377964473009

Circle Area = 263.893782902

Green Area / Yellow Area = 2 : 1

X = Angle AFE = 135

Triangle Area = 147

X = Line Segment DE = 2

X = AM = 5.47722557505

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a = DE = 2.82842712475

Missing Segment BE = 1

Green Area / Red Area = 2

X = BC = 8

Orange Area = 18.4245100536

Segment BE = 1

X = DF = 5

X = Angle CFE = 80

X = DE = 4

Purple Area = 7