See the figure:
All the sides of $\triangle{ABC}$ are positive integers. The greatest common factor of $a$ and $b$ is $2$. $G$ and $I$ are the centroid and incenter of the triangle. $GI \perp CI$. What is the perimeter of the triangle?
See the figure:
All the sides of $\triangle{ABC}$ are positive integers. The greatest common factor of $a$ and $b$ is $2$. $G$ and $I$ are the centroid and incenter of the triangle. $GI \perp CI$. What is the perimeter of the triangle?