Proposed Problem
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.
Monday, February 23, 2009
Problem 254: Triangle, Centroid, Vertices, Interior/Exterior Point, Distances, Squares
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AB_ means vector AB
ReplyDeleteG 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
.-.