Enigma 359: Neat odd quad
26 August 2016
Posted by on
From New Scientist #1508, 15th May 1986 [link]
I call ABCD an odd cyclic quadrilateral, or “odd quad” for short. It has four corners A, B, C, D, and four straight sides AB, BC, CD, DA, so it’s a quadrilateral. The corners lie on a circle, so it’s cyclic. And it’s odd because — well, what is its area? I have decided to define that as what the sides cut off from the outside world, that is, the sum of the shaded areas.
A neat odd quad has the lengths of its four sides all different positive whole numbers and its area is a whole number too.
Can you find a neat odd quad with an area less than 30? What are the lengths of:
(a) The sides AB, CD, which don’t cross?
(b) The crossing sides BC, AD?