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3circles are placed on a plane in such away that each circle touches the other two. radius of each is 10cm.find the region enclosed by the them




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If we join the centers of three circles, it will be an equilateral triangle of side length 20 cm.
now, area of equilateral triangle = √3/4 ×(20)² =1.732 ×100 = 173.2 cm²
now, area of the 3 sectors of three circles = 3×π ×(10)²×(60°/360°)
                                          = 50 π
                                          = 157 cm²
area of the region enclosed =( 173.2 - 157 )cm² = 16.2 cm²
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