In triangle \(ABC\) equilateral triangles \(ABX, BCY,\) and \(ACZ\) are constructed.

Prove that \(AY = BZ = CX\) and that all three lines are concurrent at \(O\).

In triangle \(ABC\) equilateral triangles \(ABX, BCY,\) and \(ACZ\) are constructed.

Prove that \(AY = BZ = CX\) and that all three lines are concurrent at \(O\).

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