# The area of two intersecting circles.

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.

• Hint: $CD=12$ by Pythagoras theorem. – Tunk-Fey May 26 '14 at 17:45
• See this Area of intersection between two circles. It can help you. – Jika May 26 '14 at 17:48
• @Jika In that question, the circles are a radius distance apart. – usama8800 May 26 '14 at 17:53
• Yes but it is simply a hint. It can give you a way of thinking to solve your problem. @usama8800 – Jika May 26 '14 at 18:00
• @Tunk-Fey thanks, I got it. – usama8800 May 26 '14 at 18:06

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 $B$.