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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