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Six six four
Two regular hexagons and a square. What’s the angle α?
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Pentagon divided
Given a pentagon ABCDE, construct the points T,R,Q,U such that the segments AT, AR, AQ, and AU divide the pentagon into five equal area pieces. (Using straight edge and compass. But you may divide a segment into a number of equal segments for free.)
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Video: Triangle offspring
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Square offspring
Three squares and two line segments. What’s the angle α?
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Video: No laughing matter
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Squaring a rectangle II
A square contains a red rectangle with an extended side. Prove that red=|AB||AC|+|BE||CD|. By Matthew Arcus.
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Two medians and one side
A triangle has sides a,b,c and the medians d,e,f ending at those sides, respectively. Given only the lengths (b,d,e) construct the triangle (a,b,c). (Start with a triangle with side lengths determined in some manor from the given 3 lengths.)
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Video: Unring a bell
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Pentagon offspring
Three regular pentagons are placed as shown. Prove that the three black line segments are concurrent.