A regular pentagon, two semicircles and two chords. What’s the length proportion a : b?
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Crazy frog
Author: Rik D. Tangerman
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Composition in red, blue and yellow
A rectangle containing red and blue squares and a yellow rectangle. What is the proportion red : (blue+yellow)?
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The dark lord
Two congruent equilateral triangles and two squares. What’s the angle α?
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The pointy shoe
A quarter circle, a semicircle and a triangle. What’s the angle α?
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Cordon sanitaire
Two perpendicular lines and a third line. Four circles are tangent to all three lines. Prove that their areas satisfy AB=CD.
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The green zone
A quarter circle and a right triangle inside a square. One of the vertices of the triangle is the square’s centre. What fraction of the square’s area is green?
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The open book
Three squares share four vertices. What is the proportion of the line segment lengths a and b?
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The kissing circles
A rectangle with three touching quarter circles. What fraction of its area is coloured?
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The balancing act
A square with two perpendicular lines. What is the minimal blue fraction?
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The commons
Two touching circles and a common tangent. Three triangles are formed by tangency points and centres. What is the area of the green triangle X in terms of areas A and B?