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Question
The radius of a circle is 20 cm. It is divided into four parts of equal area by drawing three concentric circles inside it. Then, the radius of the largest of three concentric circles drawn is
Options
10 \[\sqrt{5}\]
10\[\sqrt{3}\]cm
10\[\sqrt{5}\]
10\[\sqrt{2}\]
Solution
The circle can be divided into four parts of equal area by drawing three concentric circles inside it as,
It is given that OB = 20 cm. Let OA = x.
Since the circle is divided into four parts of equal area by the three concentric circles, we have,
Area of the fourth region `=1/4xx`Area of the given circle
`pixx(20^2-x^2)=1/4xxpixx20^2`
`400-x^2=100`
`x^2=300`
`x-10sqrt3 cm`
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