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CMO 1981 Problem 2

  • Paper

Given a circle of radius rr and a tangent line ℓ\ell to the circle through a given point PP on the circle. From a variable point RR on the circle, a perpendicular RQRQ is drawn to ℓ\ell with QQ on ℓ\ell . Determine the maximum of the area of triangle PQRPQR .

Dataset text AI-MO AoPS. Quoted with source.

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