Several line segments, some of which are parallel. What is green : orange?
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Euclid’s wing
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The mirror box
Light rays bounce off mirrored walls of a square before reaching one of the other corners. What are the slopes of the light rays leaving A that land in one of the corners B or D after exactly k=5 reflections?
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Dancing squares
Four squares and one centre. Prove that the red quadrilateral is a parallelogram.
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Making a dent
A right triangle with one trisected angle. What’s the angle α?
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Mix master
What is the sum of the angles at the blue vertices of this 11-gon?
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A central angle
One blue and two congruent red squares. The shown point is the red square centre. What is the angle α?
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The gondola lift
A tangent and its normal in an arbitrary point on an ellipse with eccentricity e. The focal points are also shown. What is the minimum value of blue : red in terms of e?
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Pines and sky
Show that the light blue area is the same as the dark green area.
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The tetromino
A square, its diagonal and six smaller squares. What fraction is purple?
What is the full bat area (including the enclosed white parts) divided by that of its (equilateral triangular) upper torso?