Optimization Problem in Acute Angle
What is it about?
A Mathematical Droodle

Let a point A lie in the interior of an acute angle. Find points B and C on the sides of the angle (one per side) such that the perimeter of ΔABC is minimal.

Let A_B and A_C be the reflections of A in the sides of the angle. Then the perimeter of ΔABC equals AB + BC + CA = A_BB + BC + CA_C. The latter is never shorter than the distance between A_B and A_C, so that

AB + BC + CA ≠ A_BA_C.

The equality is achieved when B and C are chosen to be the points of intersection of the corresponding sides of the angle with A_BA_C.