Quote:
Originally Posted by fetofs
A typo, perhaps? RH and HC should make an X, unless I miss something.
P.S: A clearer drawing could've helped me see some things. The triangle AMN is similar to triangle ABC, in the sense that is only scaled down. AM/2 = AB, MN/2 = BC and AN = AC/2, therefore their angles are equal.

:smile
Yes you are right fetofs. It was meant to be RN // HC. Hence Triangle ARN is similar to triangle AHC.
Agreed: A good figure (362436 inclusive!) is half the solution to the problem.
Your proportions are entirely wrong; AB = 2 AM, BC = 2 MN and AC = 2 AN
This similarity does not get you very far.
Given details are never superfluous and you must make use of the given orthocentre. Hence I have used the triangle AHC also which is important for the proof.
Im sorry I dont know how to make diagrams on the pc. Otherwise I would have given one for clarity.
Regards, and feel free to send some more problems from BMO (whatever that is)
Mally