A regular dodecagon and three equilateral triangles. What’s the proportion purple : green?
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The crown jewel
Tag: triangle
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Ceteris paribus
Three circles with their centres and a triangle ABC. Given that D is the midpoint of BC, prove that quadrilateral ABEF and triangle ECF have both equal perimeter and equal area.
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The pendulum
Two equilateral triangles share a side midpoint. What is the angle α?
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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 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?
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The night sky
A semicircle containing two equilateral triangles and a circle. What’s the yellow fraction?