Andrey Dyukmedzhiev
7/8/2017 10:40:19 am
The blue area is 1/9 of the colored region area (triangular area); the green area is 8/9, as shown here:
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tom
7/8/2017 05:57:48 pm
Call the radius of the semicircle x, The the width of the rectangle is 2x and its height is x√2. The height of the top of the green part is xsin(2α)= 2xsin(α)cos(α) = 2xtan(α)cos²(α) = 2x√2 /sec²(α) = 2x√2/(1+tan²(α)) = 2x√2/3, leaving x√2 - 2x√2/3 = x√2/3 for the height of the blue triangle. So the similar triangles
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