Task 560
Task 560: development task in emrekuruu/math-openenv, an RL environment on the Hugging Face Hub. Circles $A,B$, and $C$ are externally tangent to each other and internally tangent to circle $D$. Circles $B$ and $C$ are congruent. Circle $A$ has radius 1 and passes through the center of $D$. What…
The task
Circles $A,B$, and $C$ are externally tangent to each other and internally tangent to circle $D$. Circles $B$ and $C$ are congruent. Circle $A$ has radius 1 and passes through the center of $D$. What is the radius of circle $B$? [asy]unitsize(1cm); pair A,B,C,D; A=(-1,0); B=(0.66,0.88); C=(0.66,-0.88); D=(0,0); draw(Circle(A,1),linewidth(0.7)); draw(Circle(B,0.88),linewidth(0.7)); draw(Circle(C,0.88),linewidth(0.7)); draw(Circle(D,2),linewidth(0.7)); label("$A$",A,A); label("$B$",B,B); label("$C$",C,C); label("$D$",(-1.2,1.6),NW); [/asy]