Consider three circular parks of equal size with centres at A1, A2 and A3 respectively. The parks touch each other at the edge as shown in the figure (not drawn to scale). There are three paths formed by the triangles A1A2A3, B1B2B3 and C1C2C3 as shown. Three sprinters A, B, and C begin running from points A1, B1 and C1 respectively. Each sprinter traverses her respective triangular path clockwise and returns to her starting point.
Sprinters A, B and C traverse their respective paths at uniform speeds of u, v and w respectively. It is known that u2:v2:w2 is equal to Area A:Area B: Area C, where Area A, Area B and Area C are the areas of triangles A1 A2 A3, B1 B2 B3, and C1 C2 C3 respectively. Where would A and C be when B reaches point B3?