A square is divided by six line segments. What fraction is brown?
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The chess board
A unit circle with an inscribed square and four semicircles. What’s the sum of the semicircle areas?
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The Olympic bowl
A parabola is tangent to the equal sides of an isosceles triangle in its equal vertices. Another tangent is drawn as shown. Prove that the red line segments are congruent.
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As above, so below
A semicircle, a square, a triangle and two circles. A centre and a tangency point are highlighted. Prove that the circles are congruent.
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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 full circle
Two squares of area D and J share a vertex while the circle passes through four other vertices. What is the area of the latter in terms of D and J?
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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?