Here is the link to the problem:

https://icpcarchive.ecs.baylor.edu/index.php?option=onlinejudge&page=show_problem&problem=2861

With a little searching I found out that such point for a triangle is called a Fermat/Torricelli Point, but I couldn't find a specific algorithm or any implementation for it.

Also, in the editorial for this contest, a single line is written saying that this could be solved using Lami's Theorem(in Physics).

I wasn't able to figure out a solution.

Please Help !

Thanks