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## Hex division II

A regular hexagon and two equals angles. What is blue : green : red?

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## Skimpy bathing suit

An equilateral triangle with a circle through one vertex, and the intersections FIHJ of the extended sides with the circle. Lengths of three of the external segments are indicated. What is the fourth length?

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## Mother’s umbrella II

A circle with several line segments. The red one is tangent. What’s red : green?

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## Distant Alp II

A square with its diagonal. Prove that the three red points are collinear.

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## Bullseye

Blue and orange concentric circles intersect a vertical line in green dots. Show that the dots are equally spaced, given that the red intervals shown are of equal length. (The largest circle has radius 2u.)

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## Hidden parallelogram

Blue circle (ACDGB) with CEG || AB. Pink circle (EDG) intersects AB at I. Extend DI to intersect blue circle at J, then JC intersects AB at M. Show that IM = CE.

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What is the area of the entire figure (in terms of x) given that the segments AB, CD, EF,…, QR are all semicircle diameters, and the lengths decrease geometrically ( AB=2, CD = 2x, EF= 2x^2, GH = 2x^3,…)?

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## Double eclipse

Given green and blue discs, construct a red region so that for every ray leaving L stays in the blue region exactly as long as it does in the pink region. (Namely, KM = OL.)

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## Steam roller

Two intersecting circles. Express the lengths b and the common tangent d in terms of c (the distance between the centres) and the angles β and γ.

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## Pentagon pleasure

Two regular pentagons. The centre of the large one is a vertex of the small one. What is yellow : green?