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sum of distances of interior point of rectangles >= 2 area (Chile 1993 P6)

Source:

May 27, 2019
geometryrectangledistancearea of a triangle

Problem Statement

Let ABCD ABCD be a rectangle of area S S , and P P be a point inside it. We denote by a,b,c,d a, b, c, d the distances from P P to the vertices A,B,C,D A, B, C, D respectively. Prove that a2+b2+c2+d2≥2S a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2\ge 2S . When there is equality?
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