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problem: https://toph.co/p/problem-number-nine-and-three-quarter solution: http://ideone.com/RYkF3m
though I solved it in two different ways. but I can't understand this solution. I tried but couldn't make a communication with the actual writer of the solution. Please help me.
Add auxiliary lines as plotted above.
Since
, lines NH and MB are parallel. Therefore 
.
Therefore
.
Not necessarily the most elegant way, but hope it helps anyway.
By the way do you know a better way(more elegant)? I solved it by solving equation for two straight line intersecting in a common point.
No, but I suppose two auxiliary lines won't overcomplicate it.