Let ABC be a triangle and an interior point M. We denote by AM =x_{1}, BM = x_{2}, CM = x_{3}. The distances of the point M from BC, CA, AB are denoted by p_{1}, p_{2}, p_{3}. Erdos-Mordell inequality asserts:

x_{1} + x_{2} + x_{3} no less than 2[p_{1} + p_{2} + p_{3}]

The above problem proposed by P.Erdos in the American Mathematical Monthly in 1935 and solved byI.J.Mordell and D.F.Borrow in 1937. Later many Mathematicians obtained solutions and for a long time the problem was in the air.

For some more solutions you can download my paper on the Erdos-Mordell Inequality.