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# Circles

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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.

Jun 21, 2021

#2
+33360
+3

See image below

1/4 of the circle    minus the triangle is 1/2 of the shaded area

1/4 of the circle    1/4 pi (12^2)  = 36pi

area of triangle   1/2 *  12 * 12 = 72

36 pi  - 72      * 2     =   72pi - 144 = ____________ units2

Jun 21, 2021

#1
+2097
+1

I really need to figure out how to make diagrams.... sorry if this is confusing.

Notice that 1/2 of the grey space is 1/4 of a circle - the right triangle.

So the total area of the grey space is 2(6^2*pi/4 - 6*6/2).

2(6^2*pi/4 - 6*6/2) = 18pi - 18

=^._.^=

Jun 21, 2021
#3
+2097
+1

Edit:

I'm wrong, the raduis is 12, not 6.

=^._.^=

catmg  Jun 21, 2021
#2
+33360
+3

See image below

1/4 of the circle    minus the triangle is 1/2 of the shaded area

1/4 of the circle    1/4 pi (12^2)  = 36pi

area of triangle   1/2 *  12 * 12 = 72

36 pi  - 72      * 2     =   72pi - 144 = ____________ units2

ElectricPavlov Jun 21, 2021