# Perimeter of two overlapping circles

How do I find the perimeter of these overlapping circles?

• Observe that the triangle formed by the two centers and one of the points of intersection of the two circles has sides $9,12,15$, which satisfies Pythagoras. Therefore, it is a right angle triangle. Therefore, the angles are $\pi/2, \arctan(4/3)$ and $\arctan(3/4)$. The double of the last two multiplied by the corresponding radii give you the lengths of those arcs that you need to subtract – logarithm May 13 at 15:04
• I got $99.8...$ – J. W. Tanner May 13 at 15:27
Denote the points of intersection of the circles as $$A$$ and $$B$$ and the centers as $$O_1$$ and $$O_2$$.
In triangle $$O_1AO_2$$ you have three sides so you can find the angles. Then from the information about the angles and the radii of circles you can find the arc lengths and the perimeter.