inequality
Source: Ukraine 1997 grade 9
July 21, 2009
inequalitiesgeometry proposedgeometry
Problem Statement
Triangles and are non-congruent, but AC\equal{}A_1 C_1\equal{}b, BC\equal{}B_1 C_1\equal{}a, and BH\equal{}B_1 H_1, where and are the altitudes. Prove the inequality:
a \cdot AB\plus{}b \cdot A_1 B_1 \le \sqrt{2}(a^2\plus{}b^2).