IMO 1971 LL BUL6

Origin: BUL

Problem

Let squares be constructed on the sides BC, CA, AB of a trian- gle ABC, all to the outside of the triangle, and let A1, B1, C1 be their cen- ters. Starting from the triangle A1B1C1 one analogously obtains a triangle A2B2C2. If S, S1, S2 denote the areas of triangles ABC, A1B1C1, A2B2C2, respectively, prove that S = 8S1 −4S2.