Task 375

Task 375: development task in emrekuruu/math-openenv, an RL environment on the Hugging Face Hub. In triangle $ABC$, $AB = 5$, $BC = 4$, and $CA = 3$. asy defaultpen(1); pair C=(0,0), A = (0,3), B = (4,0); draw(A--B--C--cycle); label("$A$",A,N); label("$B$",B,E); label("$C$",C,SW); /asy Point…

The task

In triangle $ABC$, $AB = 5$, $BC = 4$, and $CA = 3$. [asy] defaultpen(1); pair C=(0,0), A = (0,3), B = (4,0); draw(A--B--C--cycle); label("$A$",A,N); label("$B$",B,E); label("$C$",C,SW); [/asy] Point $P$ is randomly selected inside triangle $ABC$. What is the probability that $P$ is closer to $C$ than it is to either $A$ or $B$?