Let the circles
![k_1](/media/m/3/5/6/35656cbf3adb55dddd30996fc068363b.png)
and
![k_2](/media/m/6/a/b/6abbe24dbf6713b55498fe55ab050d06.png)
intersect at two points
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
and
![B](/media/m/c/e/e/ceebc05be717fa6aab8e71b02fe3e4e3.png)
, and let t be a common tangent of
![k_1](/media/m/3/5/6/35656cbf3adb55dddd30996fc068363b.png)
and
![k_2](/media/m/6/a/b/6abbe24dbf6713b55498fe55ab050d06.png)
that touches
![k_1](/media/m/3/5/6/35656cbf3adb55dddd30996fc068363b.png)
and
![k_2](/media/m/6/a/b/6abbe24dbf6713b55498fe55ab050d06.png)
at
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
and
![N](/media/m/f/1/9/f19700f291b1f2255b011c11d686a4cd.png)
respectively. If
![t\perp AM](/media/m/d/7/f/d7f2d940c21b2ca43ac853e4852c01c7.png)
and
![MN=2AM](/media/m/5/6/e/56e1ea0f461457058381a27a82658ae3.png)
, evaluate the angle
![NMB](/media/m/0/4/a/04a32374c7188633079aa115169ee5eb.png)
.
%V0
Let the circles $k_1$ and $k_2$ intersect at two points $A$ and $B$, and let t be a common tangent of $k_1$ and $k_2$ that touches $k_1$ and $k_2$ at $M$ and $N$ respectively. If $t\perp AM$ and $MN=2AM$, evaluate the angle $NMB$.