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Beginner

The voting pencil

A square and a rectangle share a vertex. Two triangle areas are given. What is the total area?

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Beginner

The pentagon attack

Two regular pentagons and two diagonals. What’s the angle α?

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Beginner

Confined enclosure

A square containing four smaller squares. What fraction of its area is orange?

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Lean on me

Two squares and two diagonals. Prove that the angles α and β are equal.

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Beginner

The dolphin

Two semicircles, a tangent and an altitude to the tangency point. Prove that the red triangle is isosceles.

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Beginner

Parallelism

A trapezium with its diagonals and a parallel line segment. What’s the proportion blue : red?

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Beginner

The Common Brimstone

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

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Tension control

Three squares and a line segment of which a vertex is the midpoint. What is the proportion purple : green?

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Beginner

The pyramid scheme

Two congruent circles and a triangle. Prove that the triangle is isosceles.

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Beginner

The French kiss

Two tangent circles and two red tangent line segments. The three tangency points are shown. What is the angle β in terms of the angle α?