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Advanced

Eye of the apple

A circle with an inscribed triangle with an inscribed circle. The centre of the large circle is on the small one. What fraction of the area is blue?

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Intermediate

The other half

Three semicircles with diameters a, b and x. Express x in terms of a and b.

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Beginner

The Gouda cheese

A quarter circle with two inscribed squares. What’s the angle α?

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Beginner

Three squares a day

Three congruent squares inscribed in a rectangle. What fraction of the total area is green?

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Advanced

The ice cream cone

A circle tangent to a triangle side and to the two other extended sides. What is its diameter?

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Intermediate

Similar intention

A cyclic quadrilateral and two diagonals. What fraction of its area is blue?

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Intermediate

Slip slidin’ away

Two congruent squares inscribed in a rectangle with given side lengths. What is the total orange area?

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Beginner

The glass piece

A square and an overlapping isosceles triangle. What is the angle α?

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Beginner

The red flag

Three squares of which two vertices are connected. If the red triangle has area 1.5 and the green square area 1, what is the side length x?

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Advanced

The rings

Four circles and a common tangent. The areas of the green and yellow circle are given. What are the areas of the red and blue circle?