A regular hexagon and a circle centred in the blue point. What’s the angle α?
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The pumpkin
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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?
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Three octagons
The rectangles are 3 by 4. Which of the three bounding octagons have similar shape?
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Sliding square II
A square inside a square. What fraction is pink?
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A hyperbolic style
An arbitrary point B on the unit circle is reflected in the y-axis to give B’. D is the intersection of BC and AB’. Prove it lies on the red hyperbola.
Puzzle creator: Matthew Arcus.
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Shooting the moon
Show that the blue dots are concyclic and also the orange dots are concyclic.
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The tipi entrance
A semicircle with three tangents. Prove that purple : green = red : yellow.
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Fan of cards
N coloured rectangular cards are arranged with a common vertex and common angle α between cards. If a single card has perimeter P, what is the perimeter of the coloured region, in terms of N, P, and α?
Extra condition: N and α are such that at least two edges of the bottom card are visible.