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Video: Cramped space

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Circle a ranch brand

Connect 4 (blue) points B, C, D, E on a circle to some of the (orange) midpoints of non-adjacent arcs. (For example, C connects to J, E connects to L.) Intersect CJ with EL to get F, and intersect DK with BL to get G. Show that FG || JK.

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Intermediate

Secured package

A square with several line segments. Prove that the red line segments are parallel.

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Video: The red dot

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Intermediate

The drinking bird

Two circles with two radii and two tangents. The blue line passes through points of tangency and the circle intersection. Prove that α=β.

Puzzle author: David Odell.

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Intermediate

Circle crossings

The segment CD is tangent to the green circle c, ending on the orange circle d, which also contains the foot of the perpendicular line from C to the diameter of c which extends to D. What is the angle between the two circles?

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Video: Four five

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Beginner

The leaning diamond

A square with two equilateral triangles. What’s the angle α?

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Video: Locus pocus

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Cramped space

A triangle with three circles, two of which are tangent. Prove that the upper vertex and the two tangent points are collinear.