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# geometry

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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.

Apr 14, 2022

#1
+2541
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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 $$\color{brown}\boxed{72 \pi - 144}$$

Apr 14, 2022

#1
+2541
+1

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 $$\color{brown}\boxed{72 \pi - 144}$$

BuilderBoi Apr 14, 2022