What (not-well-known) theorem is dynamically illustrated in the applet below?[br](Feel free to move the pink points and/or the brown point anywhere you'd like!) [br]
[color=#000000][b]Theorem:[/b][/color][br][br]If [color=#980000][b]perpendicular segments[/b][/color] are drawn to the sides of an equilateral triangle from [color=#980000][b]any point[/b][/color] inside that equilateral triangle, then the sum of distances from the points at which these perpendiculars meet the triangle's sides to the triangle's left-most (or right-most) vertices is always equal to half the perimeter of the equilateral triangle.