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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The mirror operation
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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?
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Five to twelve
A square and a rectangle share two vertices. If the square has twice the area of the rectangle, what’s the angle α?
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Entanglement
Two circles with two common tangents. Three red lines through tangency points and centres. Prove that they are concurrent.
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The parachute
A circular sector is divided as shown. What fraction is red?
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Polarisation
Two circles with three common tangents. Three tangency points are shown. Prove that they are collinear.
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Move the earth
A square containing a semicircle, a tangent and a line segment from the tangency point. What fraction is green?
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No pasaran
A semicircle with three tangents. The tangency points are shown. Prove that the red line segments are concurrent.
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The orange fraction
A square containing a quarter circle and a red equilateral triangle. What’s the orange fraction?