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The rotary movement

Two arbitrarily placed congruent equilateral triangles. Out of all the possible rotations of the plane, for how many will the image of ABC be A’B’C’?

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Beginner

Three folds

A square divided by three line segments. What’s the proportion yellow : purple?

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Beginner

Opposing camps

A square containing two overlapping equilateral triangles. What’s the length proportion a : b?

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Intermediate

Seeing double

Five circles, of which the green circles are congruent and so are the blue ones. If rblue : rgreen= 6, what’s rred : rgreen?

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Intermediate

Égalité

A square with its diagonal and a circle. If red is equal to blue, what’s the angle α?

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Spiegel im Spiegel

A triangle with an inscribed triangle. What fraction of the former does the latter cover in terms of lengths a, b, c, d, e and f?

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Beginner

The lever of Archimedes

Two congruent triangles are placed as shown. A line segment passes through the centroid of the yellow triangle. What’s the proportion a : b?

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Beginner

The green necktie

A square with several line segments. What fraction is green?

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Intermediate

House of Orange

A right triangle with a red and yellow square attached. Two circular arcs centered in the triangle vertices. What is the area of the orange rectangle in terms of red and yellow?

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Out of proportion

An equilateral triangle containing a parallelogram, another equilateral triangle and a circular arc that is tangent in its base vertices. What is the proportion pink : blue?