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In triangle $ABC$, $D$ is the midpoint of $AC$ and $E$ is the midpoint of $AB$. $BD$ and $CE$ are perpendicular to each other and intersect at the point $G$. If $AB=7$ and $AC=9$, what is the value of $BC^2$

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Thx aryabratha now i get 26 the answer – Veany_Johnston Apr 14 '13 at 2:05
    
If you find that it answers your question, you should accept it. – Sawarnik Feb 9 '14 at 4:58

Hint:

Use the fact that the centroid divides the medians in the ratio $2:1$

Let $BG = 2y, GD = y$ and $CG=2x, GE=x$.

Now try to use the fact that they are perpendicular. Express $BC^2$ in terms of $x$ and $y$.

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