Problem A. 434. (October 2007)
A. 434. Points A, B, C lie inside the convex hexagon MNPQRS, such that the triangles ABC, NAM, PQB and CRS are similar. Let X, Y, Z be the midpoints of the line segments NP, QR, SM, respectively, and let G, K, I be the centroids of the triangles ABC, MPR and NQS, respectively. Prove that (a) If triangle ABC is equilateral then triangle GKI is equilateral; (b) Triangles ABC and XYZ are similar if and only if triangle ABC is equilateral.
Romanian competition problem
Deadline expired on November 15, 2007.
8 students sent a solution. 5 points: Huszár Kristóf, Korándi Dániel, Lovász László Miklós, Nagy 235 János, Nagy 314 Dániel, Tomon István, Wolosz János. Unfair, not evaluated: 1 solution.