Two squares and a rectangle. What is area of the rectangle in terms of square sides a and b?
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The red sash
Category: Intermediate
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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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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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The last wave
A square containing a quarter circle, a semicircle and a circle. What is the proportion blue : green?
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The tightrope dancer
A circle containing an isosceles and two equilateral triangles. What is the proportion orange : blue?
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The hidden pyramid
A triangle with an inscribed equilateral triangle. If areas A and B add up to C, what are the proportions A : B : C?
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Down to earth
Two equilateral triangles share a vertex. What is the proportion red : green?
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The residue
A parabola is tangent to two sides of a square and to the hypotenuse of an isosceles triangle. The three tangency points are shown. What fraction of the square is green?
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Jingle bells
Two equilateral triangles share a vertex. What is the area of their overlap region?
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Lost in rotation
Four equilateral triangles inscribed in a fifth one. What fraction of the latter is coloured?