Two equilateral triangles share a side midpoint. What is the angle α?
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The pendulum
Month: October 2022
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The misfit
A rectangle is inscribed in a regular hexagon, covering 14/27 of its area. What is red : yellow : green?
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In orbit
The smaller circle has its centre on the larger circle and is also the triangle’s incircle. Prove that the circle centres and the triangle vertex are collinear.
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La Sagrada Familia
Two congruent right triangles on a common baseline have an overlap of variable size. What is the proportion of the minimal area to the maximal area?
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The road less traveled
What is the area of the trapezium in terms of lengths a and b?
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Cherry picking
Two quarter circles and a red circle tangent to two chords. What fraction is red?
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The hand fan
Three congruent triangles constitute a quadrilateral. What’s red : blue?
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The beam in your eye
Three parallelograms are inscribed in a circle. Prove that the common red vertex is the orthocentre of the dashed triangle.
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The mirror operation
A point P is mirrored in the midpoints of the green triangle sides. The three mirror images form a blue triangle. Prove that it is congruent to the green one.
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Pointing upwards
A square containing two equilateral triangles. What’s the proportion blue : orange?