Almost the entire argument is correct. It is true that HL < KL. But the diagram is seriously misleading. Take ABD to be approximately equilateral with C close to B. Then the points K, C Y, N lie in that order on the line KN and the points X, H, P, N, D lie in that order on the line DX. N does not lie inside ABM.
© John Scholes
jscholes@kalva.demon.co.uk
22 Sep 2002
Last corrected/updated 23 Aug 03