Let $\displaystyle A_1A_2...........A_7, B_1B_2.........B_7, C_1C_2............C_7$ be regular heptagons with areas $\displaystyle S_A, S_B, S_C$ respectively. Let $\displaystyle A_1A_2 = B_1B_3 = C_1C_4$. Prove that $\displaystyle \frac {1}{2} < \frac {S_B + S_C}{S_A} < 2 - \sqrt2$.