Bariz - Problem

Any triangle has at least two acute angles. Assume that the given triangle is $ABC$ with acute angles $A$ and $C$. 1)Construct the altitude $BH$. Since angles $A$ and $C$ are acute, point $H$ lies inside the triangle 2)Construct the midpoint of side $AC$ 3)Construct point $D$ symmetric to point $H$ wrt the midpoint of $AC$ By Pythogorean theorem it is easy to prove that the line $BD$ suffices the condition.