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.
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.
The diagram shows a regular dodecagon. What is the size of the marked angle?
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?