Four equal circles are described at …
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Naveen Sharma 7 years, 1 month ago
Ans.
Let ABCD be the square. Let r be the radius of each of the 4 equal circle that are described at each vertices of square ABCD.
Now, AB = BC = CD = DA = 2r
We know that each angle of a square is a right angle.
{tex}=> \angle A= \angle B= \angle C= \angle D = 90{/tex}
Now, area of a quadrant of the circle having centre at A = {tex}{90\over 360}\pi r^2 = {1\over 4}\pi r^2{/tex}
area of 4 quadrants = {tex}4\times {1\over 4}\pi r^2 = \pi r^2{/tex}
Area of Square = {tex}(2r)^2 = 4r^2{/tex}
Area of Shaded Region = Area of Square - Area of 4 quardants
{tex}=> {24\over 7} = 4r^2 - \pi r^2 = r^2(4-{22\over 7}){/tex}
{tex}=> {24\over 7} = r^2\times {6\over 7}{/tex}
{tex}=> r^2 = 4 => r = 2cm{/tex}
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