Four squares and two shared vertices. What fraction is blue?
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The movie film
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An irregular tiling
A triangle divided by three line segments. What fraction is blue?
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The guylines
Two squares and an extended side. What’s the angle α?
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Cross the line
An equilateral triangle with two line segments crossing exactly on the semicircle. What is the proportion red : green?
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The baby block
Two squares and an extended side. Prove that red : green = blue : yellow.
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The England win
A unit square containing two red overlapping congruent rectangles. If they cover exactly half the square’s area, what is their width x?
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A fair division
A square with a diagonal and a right triangle. What’s the proportion blue : red?
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The steam locomotive
Two tangent circles, a chord towards the tangency point and a tangent. What’s the proportion a : b in terms of radii R and r?
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The inner circle
A triangle with its incircle. A line segment through two tangency points and one through the incentre. What’s the angle α?
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Know all angles
A triangle with its circumcircle and circumcentre. What’s α : β?