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Old 2006-11-03, 03:29   #11
Bronze Medalist
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Jan 2004

22×33×19 Posts
Lightbulb TYPO.

Originally Posted by fetofs View Post
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.

Yes you are right fetofs. It was meant to be RN // HC. Hence Triangle ARN is similar to triangle AHC.

Agreed: A good figure (36-24-36 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)

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