MathDB

6

Part of 1993 Chile National Olympiad

Problems(1)

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

Source:

5/27/2019
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?
geometryrectangledistancearea of a triangle