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Down to earth

Two equilateral triangles share a vertex. What is the proportion red : green?

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The sand heap

Two squares share a vertex. Three other vertices form a triangle, of which one side length is given. What is its area?

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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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Mind the gap

A regular hexagon with an equilateral triangle sharing a vertex and having a vertex somewhere along the opposite side. What is the maximum length of line segment g?

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Down the tree

Two overlapping congruent isosceles triangles. What fraction of the total area is green?

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The leftover package

An isosceles triangle with an inscribed square and three triangles. What is the proportion black : red?

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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?

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