A semicircle with its centre. What is green : red in terms of the angles α and β?
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Through the roof
Tag: proportion
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Snow man scarf
Show that blue = red if and only if purple = orange.
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The propeller
The blue square blades are twice as long as the red triangle sides. What is the ratio of red to yellow areas?
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Connected centres
Two quarter circles and a semicircle. The blue points are quarter and semicircle centres. What is red : green?
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Seven chords
A regular 7-gon inscribed in a circle (ABCDEFG), with some other point H on the circle, in the arc CD. Show that the length sum of the blue chords equals the length sum of the green chords.
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Wild floor tile
What is the ratio of areas, purple/green, when the orange octagon is regular (all angles equal)?
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Euclid’s wing
Several line segments, some of which are parallel. What is green : orange?
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The gondola lift
A tangent and its normal in an arbitrary point on an ellipse with eccentricity e. The focal points are also shown. What is the minimum value of blue : red in terms of e?
What is the full bat area (including the enclosed white parts) divided by that of its (equilateral triangular) upper torso?
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The tipi entrance
A semicircle with three tangents. Prove that purple : green = red : yellow.