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
12 * * 9
* α β *
P * * * * * * * Q
Note that we have a 3-4-5 right triangle.
We have: .
Therefore, the external circumference is: