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min distance of projections in a triangle 4-5-6

Source: Israel Grosman Memorial Mathematical Olympiad 2001 p4

February 15, 2020
Triangleminperpendiculardistancegeometry

Problem Statement

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?
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