Two circles with centers $A$ and $B$ of radius $10$ intersect at points $B$ and $C$ such that $AB = 16$. $\angle BAC=\angle ABC = 0.64\,\operatorname{rad}$ and $\angle ACB = 1.86\,\operatorname{rad}$. The arc length $CD = 12.87$.
I need to find the area of the shaded region and I can't think of any way to do it.
Best Answer
If you draw the line segment from $C$ to $D$, it divides the shaded region into two pieces called circular segments. One of the circular segments is a segment of the circle with center at $A$, and the other is a segment of the circle with center at $B$.
You can see here -- http://mathworld.wolfram.com/CircularSegment.html -- how to compute the area of a circular segment.