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IL-GROSSMAN 2001 Problem 4

    The lengths of the sides of triangle ABCABC are 4,5,64,5,6 . For any point DD on one of the sides, draw the perpendiculars DP,DQDP, DQ on the other two sides. What is the minimum value of PQPQ ?

    Dataset text AI-MO AoPS. Quoted with source.

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