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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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