Meet equilateral triangle ABC inside which we have point P.
Point D is on AC, point E on AB, point F on BC, such that DP, EP and FP are the perpendicular distances from P to the sides;
let DP = u, EP = v and FP = w.
AP, BP and CP are the distances from the vertices;
let AP = a, BP = b and CP = c.
Let k = side lengths of the triangle.
The only givens are u, v and w.
What are the lengths of a, b, c and k in terms of u,v,w ?