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Existence of point P, A', B', C' satisfying conditions

Source:

October 14, 2010

geometry unsolvedgeometry

Problem Statement

Prove that for any triangle

ABC

there exists a point P in the plane of the triangle and three points

A' , B'

, and

C'

on the lines

BC, AC

, and

AB

respectively such that

AB \cdot PC'= AC \cdot PB'= BC \cdot PA'= 0.3M^2,

where

M = max\{AB,AC,BC\}