Date: Wed, 20 Nov 1996 18:38:45 -0500

From: Alex Bogomolny

Dear Ania:

I am pretty sure your inequality is correct but, for the moment, the proof eludes me. The problem is unusual and your taking interest in it suggests you may like Math and, probably, like solving math problems. While I am looking into your inequality would not you like to prove the following:

In a triangle ABC, the sum of heights is never less than 9 (sic!) times the radius of the inscribed circle:

_{A}+h

_{B}+h

_{C}≥9r

Sincerely,

Alexander