Hello, castle!

I marked the top of the intersection (where the 2 circles meet) "A" and the bottom "B".

Then I made a triangle with the midpoint of AB and the centre of the larger circle.

I used Sine Law to find the angles and then found the sector length.

My final answer came to be 98.89.

However my textbook has a different answer. . What is it?

Let be the center of the 12-radius circle,

. . and be the center of the 9-radius circle.

Now look at

Code:

A
*
* *
12 * * 9
* *
* *
* α β *
P * * * * * * * Q
15

Note that we have a 3-4-5 right triangle.

Hence: .

Then: .

And:

Hence:

We have: .

Then: .

And:

Hence:

Therefore, the external circumference is:

. .