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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

Best Answer 

 #1
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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
avatar+1384 
+1
Best Answer

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

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