Russian problems Problem 41 In the triangle ABC, the length of the altitude from A is not less than BC, and the length of the altitude from B is not less than AC. Find the angles.
Let k be twice the area of the triangle. Then k>=BC 2 , k>=AC 2 and k<=AC.BC, with equality in the last case only if AC is perpendicular to BC. Hence AC and BC have equal lengths and are perpendicular. So the angles are 90, 45, 45. Russian 41-50 (C) John Scholes jscholes@kalva.demon.co.uk 22 Sep 1998