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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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