Task 535
Task 535: development task in emrekuruu/math-openenv, an RL environment on the Hugging Face Hub. A circle of radius 1 is surrounded by 4 circles of radius $r$ as shown. What is $r$? asy unitsize(0.6cm); for(int i=0; i<2; ++i){ for(int j=0; j<2; ++j){…
The task
A circle of radius 1 is surrounded by 4 circles of radius $r$ as shown. What is $r$? [asy] unitsize(0.6cm); for(int i=0; i<2; ++i){ for(int j=0; j<2; ++j){ draw(Circle((-2.4+4.8i,-2.4+4.8j),2.4),linewidth(0.7)); draw((-2.4+4.8i,-2.4+4.8j)--(-0.7+4.8i,-0.7+4.8j)); label("$r$",(-1.5+4.8i,-1.5+4.8j),SE); }; } draw(Circle((0,0),1),linewidth(0.7)); draw((0,0)--(1,0)); label("1",(0.5,0),S); [/asy]