## Concurrent Congruent Segments

#### Problem

In triangle $ABC$ equilateral triangles $ABX$, $BCY$, and $ACZ$ are constructed.

Prove that $AY = BZ = CX$ and that all three lines are concurrent at $O$.

Problem ID: 309 (04 Feb 2007) Difficulty: 4 Star

In triangle $ABC$ equilateral triangles $ABX$, $BCY$, and $ACZ$ are constructed.

Prove that $AY = BZ = CX$ and that all three lines are concurrent at $O$.

Problem ID: 309 (04 Feb 2007) Difficulty: 4 Star