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sum PQ+PR+PS is independent of the choice of P interior of equilateral

Source: Norwegian Mathematical Olympiad 1997 - Abel Competition p2a

February 11, 2020
geometrySumperpendicularindependentEquilateral

Problem Statement

Let PP be an interior point of an equilateral triangle ABCABC, and let Q,R,SQ,R,S be the feet of perpendiculars from PP to AB,BC,CAAB,BC,CA, respectively. Show that the sum PQ+PR+PSPQ+PR+PS is independent of the choice of PP.
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