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cos<AOB by two tangents in trinomial (III Soros Olympiad 1996-97 R2 10.3)

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May 31, 2024
analytic geometry

Problem Statement

Let's consider the graph of a square trinomial having roots 11 and 44. Let's draw two tangents to it from point OO (the origin of coordinates), touching it at points AA and BB. What values can the cosine of angle ∠AOB\angle AOB take?
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