Task 180
Task 180: test task in emrekuruu/math-openenv, an RL environment on the Hugging Face Hub. In circle $J$, $HO$ and $HN$ are tangent to the circle at $O$ and $N$. Find the number of degrees in the sum of $m\angle J$ and $m\angle H$. asy size(150); import graph; pair J = (0,0), H = (6,0), O, N; path…
The task
In circle $J$, $HO$ and $HN$ are tangent to the circle at $O$ and $N$. Find the number of degrees in the sum of $m\angle J$ and $m\angle H$. [asy] size(150); import graph; pair J = (0,0), H = (6,0), O, N; path circ = Circle(J,3); pair M = midpoint(J--H); path secCirc = Circle(M,3); pair[] tangentPoints = intersectionpoints(circ,secCirc); O = tangentPoints[0]; N = tangentPoints[1]; draw(J--N--H--O--cycle); draw(circ); label("$H$",H,E); label("$J$",J,W); label("$N$",N,S); label("$O$",O,NE); [/asy]