A circle containing eight touching circles. Circles of equal colour are congruent. What fraction of the total area is coloured?
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All the marbles
Category: Intermediate
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Two square pegs
Two squares and a circle. What is the proportion a : b?
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The other half
Three semicircles with diameters a, b and x. Express x in terms of a and b.
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Similar intention
A cyclic quadrilateral and two diagonals. What fraction of its area is blue?
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Slip slidin’ away
Two congruent squares inscribed in a rectangle with given side lengths. What is the total orange area?
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Z
A green quadrilateral of which two sides are tangent to a quarter circle of radius r. What is its area?
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Overlapping interests
A square, a rectangle and a circle that partially overlap. One square vertex coincides with a rectangle-circle tangency point. Prove that the area of the square equals that of the rectangle.
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The rising sun
A rectangle with a circle and a semicircle. What is the proportion red : blue in terms of a and b?
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The vanishing point
A square and an equilateral triangle. An extended side and diagonal meet in a point. What is the angle α?
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The dance
A regular hexagon, two squares and a semicircle connecting two vertices. Is the red vertex located on the semicircle?