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The radii of two circles are(19;cm) and (9;cm)respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles(.)

Question

 The radii of two circles are\(19\;cm\) and \(9\;cm\)respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles\(.\)

Answer

28 cm
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Solution

Let \(r_{1}=19\;cm\) and \(r_{2}=9\;cm\)and r be the radius of new circle\(.\)
\(\therefore \)Circumference of \(1^{st}\) circle\(,\)
\(C_{1}=2\pi r_{1}=2\pi \times 19=38\pi\; cm\)
and circumference of \(2^{nd}\) circle\(,\)
\(C_{2}=2\pi r_{2}=2\times \pi \times 9=18\pi\; cm\)
According to the given condition\(,\)
Circumference of new circle \(=\) Circumference of \(1^{st}\) circle\(+\) Circumference of \(2^{nd}\) circle
\(\therefore \)   \(2\pi r=38\pi +18\pi \)
\(\Rightarrow 2\pi r=56\pi \)
 \(\Rightarrow\)\(r=\frac {56\pi }{2\pi }=28\;cm\)
Hence\(,\) radius of new circle is\(28cm.\)
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