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## The butterfly effect

Two touching circles and two lines passing through the tangency point. What is the area proportion of the two triangles?

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## The spinning top

An equilateral triangle stacked on a pentagon. What’s the angle?

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## Don Quixote and the windmill

Don Quixote is approaching a windmill. The sails of length √2 are attached to a point that is 2 above eye level. What is the maximum vertical angle that Don Quixote perceives as he moves forward?

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## The paper hat

A rectangle and several triangles. The orange triangle has the same area as the green trapezium. What’s the total coloured fraction?

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## A winter valley

A rectangle and two triangles. What’s the total area?

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## The ricochet

An isosceles triangle with base 10 and sides 13. What is the total length of the red line segments?

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## Whiskey on the rocks

Two squares share a vertex. An isosceles triangle connects three others. What fraction is blue?

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## Beware of the dots

Two congruent circles and a common tangent. A triangle connecting tangency points and the upper intersection point. What angle α maximises its area?

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## Triangular billiards

A ball track starts halfway the left side of an equilateral triangular billiard table having side length 2. After two bounces it arrives in the top corner. What’s the total track length?

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