A semicircle with three tangent line segments. What is its area in terms of lengths a and b?
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Colour confinement
Month: October 2021
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Two steps forward
Two equilateral triangles share a vertex and have their bases on the same line. A third equilateral triangle is constructed from their apexes. Prove that its apex is also on that line.
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The earth projection
A circle touching a semicircle and a triangle. What is the proportion blue : green?
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Crazy frog
A regular pentagon, two semicircles and two chords. What’s the length proportion a : b?
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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?