# How far until it won't come back?

Three identical discs A, B, and C are on a smooth horizontal plane. The disc A is set in motion with velocity $$v$$ after which it experiences an elastic collision simultaneously with discs B and C. The distance between the centers of discs B and C prior to the collision is $$\eta D$$ where $$D$$ is the diameter of a disc.

Find the largest value of $$\eta$$ such that disc A recoils to the left after the collision.

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