This is an interesting problem which takes in several different forms.
Graph the 2 circles. The radius of the larger is 11/2 and of the smaller is 2.
The right point of intersection occurs when sin θ = 4/11 so that θ is approximately 21.32º.
Notice that the central angles subtended by the common chord are equal.
That central angle is about 137.36º = 2(90-21.32).
Thus the arc of each circle involved is 137.36/360 of the circumference.
You now have all the information necessary to compute the arc length of each arc and thus the required perimeter,
12/7/2022
I made a TERRIBLE mistake in this problem.
The 2 central angles are NOT equal!!!!
137.36° is the central angle for the smaller circle.
Some construction will get the central angle of the larger circle, namely 85.29°.
With that information you can easily get the perimeter of the lenticular area.
I apologize for making this error and hope you either found or were told or shown error!
