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Question 7
Three circles each of radius 3.5 cm are drawn in such a way that each of them touches the other two . Find the area enclosed between these circles.

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Solution



Given that, three circles are in such a way that each of them touches the other two now. We join centre of all three circles to each other by a line segment. Since, radius of each circles is 3.5 cm,

So, AB=2×Radius of circle

=2×3.5=7 cm

AC=BC=AB=7 cm

Which shows that, ΔABC is an equilateral triangle with side 7 cm.

We know that each angle between two adjacent sides of an equilateral triangle is 60.

Area of sector with angle A=60

=A360×πr2=60360×π×(3.5)2

So, area of each sector = 3 × Area of sector with angle A

=3×60360×π×(3.5)2

=12×227×3.5×3.5

=11×510×3510=112×72

=774=19.25 cm2

Area of ΔABC=34×Side2
=34×72=21.21

Area of the shaded region

= Area of the equilateral triangle - Area of three sectors

=21.21761925=1.9676 cm2

Hence, the required area enclosed between these circles is 1.967 cm2 (approx)

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