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Advanced

The ocean sunset

A semicircle is inscribed in a rectangle. What is the minimal covered fraction?

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Intermediate

Triple dice

An equilateral triangle with three congruent squares. What’s the angle α?

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Intermediate

Paper hat II

Two overlapping congruent right triangles. If |AB|=15 and |BC|=7, what is the total area?

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Beginner

The wall

Two congruent rectangles and squares. Proof that the four points are on one circle.

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Beginner

The pentagon push

Two regular pentagons share a vertex. What’s the angle α?

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Intermediate

En garde

An isosceles triangle with two altitudes dividing each other in segments of length 4 and 5. What is the total triangle area?

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Advanced

The satellite

A circle containing three squares. What fraction is coloured?

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Intermediate

Distant peaks

Two isosceles triangles and a right angle. What is the proportion green : gold?

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Beginner

The blue pill

A regular octagon containing a blue hexagon. All line segments have equal length. What fraction is blue?

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Intermediate

The Lion King II

A regular hexagon and three squares. What is the proportion yellow : brown?