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See the figure:

enter image description here

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?

r ne
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    What are the upvotes for? Is it for posting a question that doesn't seem easy to solve? (It has a straightforward approach given the right triangle). Please upvote posts that show efforts and OP's willingness to interact and contribute a discussion/topic to the site. – cosmo5 Feb 24 '21 at 18:56
  • I have no idea about the meaning of upvoting a question... – r ne Feb 24 '21 at 19:15
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    https://math.stackexchange.com/questions/1593075/how-to-prove-that-6ab-ababc-for-triangle can help. – Tan Feb 24 '21 at 19:17
  • @rne Please read the guidelines on how to ask a good question. – cosmo5 Feb 24 '21 at 19:18
  • @Tan Thank you! This is great reference. May I know how did you search a question on this site? is it possible to search existing questions? – r ne Feb 24 '21 at 20:51
  • @cosmo5 Thanks! Just updated the title – r ne Feb 24 '21 at 20:54
  • You can use https://approach0.xyz/search/. Not only for this site, you can use it for any kind of mathematical search. – Tan Feb 24 '21 at 20:56

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