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Beginner

That hill

A triangle is divided in three smaller triangles. What is the proportion yellow : green?

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Intermediate

Two square pegs

Two squares and a circle. What is the proportion a : b?

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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.

Categories
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?

Categories
Intermediate

Similar intention

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

Categories
Intermediate

Slip slidin’ away

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

Categories
Beginner

The glass piece

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