Task 155
Task 155: test task in emrekuruu/math-openenv, an RL environment on the Hugging Face Hub. Rectangle $ABCD$ has center $O$ and $AB/AD=k$. A point is randomly chosen from the interior of rectangle $ABCD$. What is the probability that it is closer to $O$ than to any of the four vertices? asy…
The task
Rectangle $ABCD$ has center $O$ and $AB/AD=k$. A point is randomly chosen from the interior of rectangle $ABCD$. What is the probability that it is closer to $O$ than to any of the four vertices? [asy] size(200); draw((-250,100)--(250,100)--(250,-100)--(-250,-100)--cycle); dot((0,0)); label("$O$",(0,0),N); label("$A$",(-250,100),NW); label("$B$",(250,100),NE); label("$C$",(250,-100),SE); label("$D$",(-250,-100),SW);[/asy]