Inscribed Trapezoids


Two trapezoids are inscribed in the same circle.

One has sides (1, 1, 1, x)

The other has sides (x,x,x,1)

What is the diameter of the circle?

Hint: Try exploring how to construct the two inscribed trapezoids by using GSP or Geogebra.


Is there more than one possible construction with different size circles?



Reference: Problem Section: School Science and Mathematics, Vol 111, No. 3, March 2011, Problem 5153.