A regular octagon with two diagonals and two squares. What’s the area proportion of the blue to the red square?
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Eight corners
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The crown jewel
A regular dodecagon and three equilateral triangles. What’s the proportion purple : green?
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The bear trap
A semicircle with two tangents and a perpendicular line segment from a tangency point. What is the blue area in terms of lengths a and b?
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The oppressed minority
A square with two inscribed squares. What is the maximal proportion green : blue?
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Ceteris paribus
Three circles with their centres and a triangle ABC. Given that D is the midpoint of BC, prove that quadrilateral ABEF and triangle ECF have both equal perimeter and equal area.
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Easing it down
Three squares share three vertices. What’s the angle α?
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The pendulum
Two equilateral triangles share a side midpoint. What is the angle α?
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The misfit
A rectangle is inscribed in a regular hexagon, covering 14/27 of its area. What is red : yellow : green?
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In orbit
The smaller circle has its centre on the larger circle and is also the triangle’s incircle. Prove that the circle centres and the triangle vertex are collinear.
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La Sagrada Familia
Two congruent right triangles on a common baseline have an overlap of variable size. What is the proportion of the minimal area to the maximal area?