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The sum of the radii of two circles is 140cm and the difference of their circumference is 88cm. Find the diameters of the circles.
Areas Related To Circles | CBSE | Class 10 | Exercise 15.1 | Maths | RD Sharma
The sum of the radii of two circles is 140cm and the difference of their circumference is 88cm. Find the diameters of the circles.

Assume the radii of the two circles be {{r}_{1}} and {{r}_{2}}

Then, the circumferences of the two circles be {{C}_{1}} and {{C}_{2}}.

We know that, circumference of circle (C) =2\pi r

Given in the question that,

Sum of radii of two circles i.e., {{r}_{1}}+{{r}_{2}}=140cm … (i)

Difference of their circumference,

{{C}_{1}}-{{C}_{2}}=88cm

2\pi {{r}_{1}}-2\pi {{r}_{2}}=88cm

2\left( 22/7 \right)\left( {{r}_{1}}-{{r}_{2}} \right)=88cm

\left( {{r}_{1}}-{{r}_{2}} \right)=14cm

{{r}_{1}}-{{r}_{2}}+14….. (ii) 

Substituting the value of  in equation (i), we have,

{{r}_{2}}+{{r}_{2}}+14=140

2{{r}_{2}}=140-14

2{{r}_{2}}=126

{{r}_{2}}=63cm

Substituting the value of r2 in equation (ii), we have,

{{r}_{1}}=63+14=77cm

Now,

Diameter of circle 1=2{{r}_{2}}=2\times 77=154cm

Diameter of circle 2=2{{r}_{2}}=2\times 63=126cm

i

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