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Center Path

Four rods of equal length are hinged at their endpoints to form a rhombus. The diagonals meet at X. One edge is fixed, the opposite edge is allowed to move in the plane. Describe the locus of the point X and prove your assertion.

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The Cyclic Quadrilateral

This gives a short summary of the properties and theorems of cyclic quadrilaterals and links to some practical examples to be found elsewhere on the site.

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Dodecagon Angles

Weekly Problem 50 - 2012
The diagram shows a regular dodecagon. What is the size of the marked angle?

Tied Up

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2
triangular field

A one hectare field is in the shape of a right angled triangle. At the midpoint of each side is a post. Horace the goat is tethered at the midpoint of the hypotenuse, and two sheep, Sid and Sadie, at the midpoints of the other two sides. Each rope is just exactly long enough to allow the animal to reach two adjacent vertices. One and only one animal can reach all points in the field. Which one is it and why?