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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Seven chords
Tag: proportion
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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.
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Bullet train
What is the ratio of orange and green areas? (The orange triangle is 45-45-90)
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Tilted hourglass III
A regular hexagon, a circle through its red centre and two line segments. What’s blue : orange?
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Primary colours
An equilateral triangle inside a rectangle. What is red : yellow : blue?
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Mountain roads
A circular mountain peak has coordinates (0,0,3) and its base has towns C=(-4,0,0), E=( 4,0,0) on opposite sides. Town D=(0,4,0) is halfway between them, around the base. A road goes partially up and down the mountain connecting C and E. Another road connects C and D. Both roads are shortest possible. What is the ratio of the road lengths?