The center of a circle is at a vertex of an equilateral triangle as shown. If the area of the circle and the equilateral triangle are both 10, what is the combined area of the two gray regions?
+2668 The area of the shaded region is the sum of the circle and triangle minus the white region.
The white region is a 60-degree sector, so its area is \({10 \times {60 \over 360}} = {5 \over 3}\)
This means that the area of the shaded region is \(20 - {5 \over 3 } = {\color{brown}\boxed{55 \over 3}}\)
