Monday, February 23, 2009

Problem 254: Triangle, Centroid, Vertices, Interior/Exterior Point, Distances, Squares

Proposed Problem
Problem 254. Triangle, Centroid, Vertices, Interior/Exterior Point, Distances, Squares.

See complete Problem 254 at:
gogeometry.com/problem/p254_triangle_centroid_squares_interior_point.htm

Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

1 comment:

  1. AB_ means vector AB
    G centroid of ABC then GA_+GB_+GC_=0_
    EA_=EG_+GA_
    EA²=EG²+GA²+2EG_.GA_
    the same way
    EB²=EG²+GB²+2EG_.GB_
    EC²=EG²+GC²+2EG_.GC_
    hence
    EA²+EB²+EC²=3m²+GA²+GB²+GC²
    .-.

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