Question 140
A point $X$ lies inside an isosceles right triangle $ABC$ with $\angle B = 90^\circ$.
Prove the inequality $AX + BX + \sqrt{2}CX \ge \sqrt{5}AB$ and find all points $X$ for which the equality holds.
Prove the inequality $AX + BX + \sqrt{2}CX \ge \sqrt{5}AB$ and find all points $X$ for which the equality holds.