Proposed Problem

See complete Problem 253 at:

gogeometry.com/problem/p253_triangle_centroid_squares.htm

Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

## Sunday, February 22, 2009

### Problem 253: Triangle, Centroid, Vertices, Distances, Squares

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da=2ma/3; db=2mb/3; dc=2mc/3 and the mediane's theorem for ma, mb, mc.

ReplyDeleteJust to complete the earlier comment:

ReplyDeletec^2+a^2-b^2/2=2*9/4*d(b)^2

b^2+c^2-a^2/2=2*9/4*d(a)^2

b^2+a^2-c^2/2=2*9/4*d(c)^2

Adding the three,

(3/2)(a^2+b^2+c^2)=(9/2)(d(a)^2+d(b)^2+d(c)^2)

or (a^2+b^2+c^2)=(3)(d(a)^2+d(b)^2+d(c)^2

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