Sunday Times Teaser 2560 – Three Trees
Published: 16 October 2011 (link)
Our front garden is circular, with a diameter less than 100 metres. Three trees grow on the perimeter: an ash, a beech and a cherry, each a different whole number of metres from each of the other two. A straight trellis 84 metres long joins the ash to the beech, and a honeysuckle grows at the point on the trellis nearest to the cherry tree. The distance from the cherry to the ash plus the distance from the ash to the honeysuckle equals the distance from the cherry to the beech.
What is the diameter of the garden?