MathDB
Problem 5 of Second round

Source: IX International Festival of Young Mathematicians Sozopol, Theme for 10-12 grade

September 22, 2018
geometry

Problem Statement

Point XX lies in a right-angled isosceles △ABC\triangle ABC (∠ABC=90∘\angle ABC = 90^\circ). Prove that
AX+BX+2CX≥5ABAX+BX+\sqrt{2}CX \geq \sqrt{5}AB
and find for which points XX the equality is met.
Back to ProblemsView on AoPS