Two quarter circles and a semicircle. The blue points are quarter and semicircle centres. What is red : green?
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Connected centres
Author: Rik D. Tangerman
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Missing an angle
A triangle with three line segments to an internal point. What’s the angle α?
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The two-state solution
Two congruent squares share a vertex. What fraction is yellow?
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Euclid’s wing
Several line segments, some of which are parallel. What is green : orange?
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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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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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The tetromino
A square, its diagonal and six smaller squares. What fraction is purple?
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The pumpkin
A regular hexagon and a circle centred in the blue point. What’s the angle α?