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Camera obscura

A quarter circular room is covered with mirrors. A ray of light is emitted from one corner and reflected somewhere on the opposite wall, then on the arc, before reaching the adjacent wall at a point a distance a from the light source and b from the circle centre. What is the maximum of a/b?

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Beginner

The pine forest

A square containing a quarter circle. What’s the proportion blue : brown : green?

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Advanced

The Eightfold Path

A semicircle, a square and an isosceles triangle. What’s the angle α?

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Intermediate

Tomba La Bomba

Three regular hexagons inside a circle. Two shared vertices and five vertices on the circle. What’s red : green?

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Intermediate

The augmented chord

A circle with four chords. What is the length of line segment x in terms of lengths a and b?

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Beginner

The iglo

A semicircle, a square and a chord. If the square has area 32, what is the semicircle area?

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Beginner

The dome tent

A rectangle with a diagonal and an inscribed semicircle. What is red : green : blue?

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Intermediate

The last wave

A square containing a quarter circle, a semicircle and a circle. What is the proportion blue : green?

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Intermediate

The tightrope dancer

A circle containing an isosceles and two equilateral triangles. What is the proportion orange : blue?

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Beginner

Free four

A unit circle with an inscribed square and four semicircles. What’s the sum of the semicircle areas?