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max inradii of OAP, unit circle related - 1993 Cono Sur Shortlist G10

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October 24, 2021
geometrymaxgeometric inequalityanalytic geometry

Problem Statement

Let ω\omega be the unit circle centered at the origin of R2R^2. Determine the largest possible value for the radius of the circle inscribed to the triangle OAPOAP where P P lies the circle and AA is the projection of PP on the axis OXOX.
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