Enigma 351: Four flies
From New Scientist #1500, 20th March 1986 [link]
Four unfriendly flies are sitting watching the cricket. Each is on the boundary of the ground, which is perfectly circular. Their names, in order round the edge, are At, Bet, Cot and Dut.
The length of each of the straight lines At-Bet, Bet-Cot, Cot-Dut and Dut-At is an exact whole number of flymins (this is, the flies’ unit of distance). Two of those lines actually have the same length. Furthermore, the total of these four lengths is precisely the same number as the area (in square flymins) of the quadrilateral At-Bet-Cot-Dut.
If I tell you that that area does not include the pitch (which is at the centre of the ground), can you tell me the four lengths?