Two sectors of a circle of radius 12 overlap as shown, with P and R as the centers of the respective circles. Determine the area of the shaded region.
+2666 Draw points A and B at the 2 intersection points of the circle.
The circular sector \(ABP\) has an area of \({144 \over 4} \pi = 36 \pi\)
The isoceles triangle has area \(12 \times 12 \div 2 = 72\)
This means that the area of half the sector is \(36 \pi - 72\). Multiply this by 2, and we find the circular sector has an area of \(\color{brown}\boxed{72 \pi - 144}\)
+2666 Draw points A and B at the 2 intersection points of the circle.
The circular sector \(ABP\) has an area of \({144 \over 4} \pi = 36 \pi\)
The isoceles triangle has area \(12 \times 12 \div 2 = 72\)
This means that the area of half the sector is \(36 \pi - 72\). Multiply this by 2, and we find the circular sector has an area of \(\color{brown}\boxed{72 \pi - 144}\)
