This problem is in Kiselev's Planitmetry, to prove that: In an equilateral triangle, the sum of the distances from an interior point to the sides of this triangle does not depend on the point, and is congruent to the altitude of the triangle.
After searching google for a while, I discovered that it has a name, Viviani's theorem. Anyways, the standard proof uses the concept of area, and the known formula for calculating the area of a triangle. But I don't believe that was Kiselev's intention, since, he placed the problem after the section on the midline theorems (In triangles and trapezoids), So does anybody know a way to do this? I only need a hint.
Attempt: I only found that each of these distances will be parallel to each altitude of the triangle, but couldn't use this fact in proving the theorem. In addition to that, I proved a case of the theorem, If the point lies on one of the altitudes, the proof follows from the picture.