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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