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Question
Find the radius of the circle whose circumference is equal to the sum of the circumferences of the circles having radius 15 cm and 8 cm.
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Solution
For circle with radius = 15 cm
Circumference of circle = 2πr
= `2xx22/7xx15` cm
= `660/7` cm
For circle with radius = 8 cm
Circumference of circle = 2πr
= `2xx22/7xx8` cm
= `352/7` cm
Sum of the circumferences of these two circles
= `660/7"cm"+352/7"cm"=1012/7"cm"`
If the required radius = R cm
Its circumference = 2πR
= `2xx22/7xx"R cm"`
= `44/7"R cm"`
Given, `44/7"R"=1012/7`
⇒ R =`7/44xx1012/7` cm
= 23 cm
∴ Required radius = 23 cm
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