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TOT 393 1993 Autumn A S1 max length in triangle by arc and 2 tangents

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June 12, 2024
geometrygeometric inequality

Problem Statement

Two tangents CACA and CBCB are drawn to a circle (AA and BB being the tangent points). Consider a “triangle” bounded by an arc ABAB (the smaller one) and segments CACA and CBCB. Prove that the length of any segment inside the triangle is not greater than the length of CA=CBCA = CB.
(Folklore)
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