Question 83
Consider equilateral triangle $ABC$ and suppose that there exist three distinct points $X, Y, Z$ lie inside triangle $ABC$ such that
i) $AX = BY = CZ$.
ii) The triplets of points $(A, X, Z), (B, Y, X), (C, Z, Y)$ are collinear in that order.
Prove that $XYZ$ is an equilateral triangle.
i) $AX = BY = CZ$.
ii) The triplets of points $(A, X, Z), (B, Y, X), (C, Z, Y)$ are collinear in that order.
Prove that $XYZ$ is an equilateral triangle.