What is the sum of the angles at the blue vertices of this 11-gon?
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Mix master
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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?
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The pumpkin
A regular hexagon and a circle centred in the blue point. What’s the angle α?
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The grassy knoll
A triangle with three cevians that are concurrent in an arbitrary interior point. What is the maximum value of bdf/ace?
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Crazy hat
The diameter of the semicircle is a side of a rectangle. Show that for any such rectangle, and any point along its top edge, the configuration produces three collinear red dots.
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Bottoming out
Two squares and a circle. What’s the angle α?