Mathematical and Physical Journal
for High Schools
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Problem A. 534. (April 2011)

A. 534. The sides of a triangle are a, b and c, the lengths of the corresponding medians are sa, sb and sc, respectively. Prove that \frac{s_as_b}{a^2+b^2} +
\frac{s_bs_c}{b^2+c^2} + \frac{s_cs_a}{c^2+a^2} \ge \frac98.

(Proposed by: Donát Nagy, Szeged)

(5 pont)

Deadline expired on May 10, 2011.


Statistics:

4 students sent a solution.
5 points:Backhausz Tibor, Nagy 235 János, Nagy 648 Donát.
1 point:1 student.

Problems in Mathematics of KöMaL, April 2011