I hope you can follow my labelling.
(I couldn't make a diagram of this one!)
The vertex of the angle is
Draw a line from through the centers of the circles.
It first intersects the small circle at ,
the center of the smaller circle is ,
is the point of tangency of the two circles,
the center of the larger circle is .
From C, draw a radius down to the point of tangency,
From E, draw a radius down to the point of tangency,
We have: .
In right triangle
. . Hence, the hypotenuse
Since , we have: .
. . That is: .
Therefore, the circumference of the larger circle is: . cm.