Bride's Chair Concurrency
Bride's Chair Locus
Heron or Hero (c. 10-70 AD) of Alexandria gave a proof of this result (see Hawking, S. (Ed.), 2005, God created the integers: Mathematical breakthroughs that changed history. London: Penguin Books, pp. 23-24.)
Coxexter, H.S.M. & Greitzer, S.L., 1967, Geometry Revisited. Washington: Mathematical Association gives it as an exercise on p. 84, and a proof using Ceva's theorem on p. 169.
Go to Bride's Chair General for a Generalization of the above result.
Updated, Michael de Villiers, 1 November 2010.