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

Subscribe to:
Post Comments (Atom)

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

.-.