Suppose that you are given an equilateral triangle, with x being a point in the triangle. Denote by x1, x2, x3 the distance of the point x from each side of the triangle, respectively (see accompanying figure).
(a) Prove that x1 + x2 + x3 = k, where k is the height of the triangle.
(b) Prove that this is true even if the point is located in the plane of the triangle, but not necessarily in the triangle, where the distance from the point to the side of the triangle is negative if the line on which the side lies separates the triangle from the point (in the accompanying diagram, y1 and y2 are positive and y3 is negative).
(c) Describe a similar property in one-dimensional line segments.
