Hello, iamanoobatmath!

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: .

Let

In right triangle

. . Hence, the hypotenuse

Since , we have: .

. . That is: .

Therefore, the circumference of the larger circle is: . cm.