\(\qquad\)Six points are chosen on the sides of an equilateral triangle \(ABC\): \(A_1, A_2\) on \(BC, B_1, B_2\) on \(CA\) and \(C_1, C_2\) on \(AB,\) such that they are the vertices of a convex hexagon \(A_1A_2B_1B_2C_1C_2\) with equal side lengths. \(\\\qquad\)Prove that the lines \(A_1B_2,\) \(B_1C_2\) and \(C_1A_2\) are concurrent.
| Attributes | Олімпіадна |
|---|---|
| Source | International Mathematical Olympiad |
| Year | 2005 |
| Number | 1 |
| Difficulty | 10.0 |
| Themes |