A regular octagon of side length 2 with two diagonals and a square. What is the purple area?
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The purple square
Category: Intermediate
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Pushing the boundary
Two equilateral triangles are placed side by side. What’s the proportion green : red?
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The Pyramid of Austerlitz
An equilateral triangle and a parabola that is tangent to two of its sides in two vertices. Proof that the triangle centre coincides with the parabola focus.
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A deep connection
Two squares inside a circle. What is the circle area in terms of length a?
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To shy away
Two squares share a vertex. What’s the proportion orange : blue?
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The domino effect
Two overlapping congruent rectangles. What’s the angle α?
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A clear vision
A circle containing a regular pentagon and two equilateral triangles. All shown points are on the circle. What’s the angle α?
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Star and stripes
Two concentric congruent squares and two red rectangles. What fraction of the total area is red?
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Letting go
Two squares share a vertex. Three other vertices are collinear. What is the area proportion of the blue to the red square?
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The double flag
Three tangent circles and a common tangent. The three tangency points are shown. What is α + β?