A triangle containing a semicircle and a circular sector centred in the right vertex. What is blue : green?
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The dirty thirties
Month: January 2023
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Scratching the surface
Three tangent semicircles and two coloured triangles. What’s the proportion yellow : green?
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The Moroni minimum
An arbitrary point on the parabola y=x2. Shown are the tangent in that point and a line segment perpendicular to it. What is the minimal height h?
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To the core
A non-isosceles triangle with a red cevian and three line segments to a point on the cevian. Prove that this point is the incentre of the triangle.
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Family ties
Two regular pentagons share a vertex. What is the proportion red : green?
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The seventh bell
A regular hexagon shares a vertex with an equilateral triangle of area 7. What is the area of the hexagon?
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Longing for spring
Four semicircles and three line segments. What’s the proportion yellow : orange?
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The common ground
Two squares share a vertex. Two other vertices are 4 units apart. A third green square has the centres as opposite vertices. What is its area?
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Rising bread
A regular hexagon with a diagonal and a circular arc centred in a side midpoint. What fraction is yellow?
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The antenna
A regular pentagon with an extended side. What’s the angle α?