[math-fun] Triangle 1/7th of generating ABC triangle

Hello Math-Fun, Draw a triangle ABC (clockwise labels) with each side devided into 3 equal parts (labels A,A1,A2,B,B1,B2,C,C1,C2): AA1=A1A2=A2B, BB1=B1B2=B2C, CC1=C1C2=C2A. Now draw AB1, BC1, CA1 -- those lines shape an "inside" triangle "I" having no common point with ABC. Question: Does an ABC triangle exist such that the surface of the inner "I" triangle is exactly 1/7th of ABC's surface? E.