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 $BC^2$
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 $y$.