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Advanced

The birdwatcher

Two congruent circles and a right triangle inside a semicircle. What fraction is blue?

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Intermediate

The tin foil hat

A circle inside a quarter circle. The triangle connects the two tangency points and the top of the quarter circle. What’s the angle α?

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Beginner

The hammock

A square inscribed in a triangle. Two areas are given. What is the square’s area?

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Intermediate

Lazy Friday

Four congruent squares plus another one. What is the angle α?

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Intermediate

The fez

A circle and a semicircle inside a square. What’s the length proportion of the two chords?

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Advanced

The orange belt

Three squares and three shared vertices. Prove that the orange quadrilateral is in fact a parallelogram.

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Intermediate

The cleaver

Four squares, a rectangle and a circle. What is the proportion brown : grey?

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Beginner

The green field

A square is divided in two quadrilaterals of given area. What fraction of the square’s perimeter is red?

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Intermediate

The twin triangles

Two squares share a vertex. Prove that the red triangle is congruent to the blue one.

Categories
Beginner

The partial eclipse

Two circles and a radius connecting their centres. What is the length of the parallel chord?