Two circles touch each other externally The sum of their areas is 490 - cm 2 Their centers are separated by 28 cm Find the difference of their radii in cm

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Two circles touch each other externally The sum of their areas is 490 $π$ cm $^{2}$ Their centers are separated by 28 cm Find the difference of their radii (in cm)

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Solution

The correct option is B 14
Let the radius of the circles be $r_{1}$ and $r_{2}$ respectively.
Area of a circle of radius r $= π r^{2}$
Given, $r_{1} + r_{2} = 28$
Also, $π {r_{1}}^{2} + π {r_{2}}^{2} = 490 π$
$=> {r_{1}}^{2} + {r_{2}}^{2} = 490$
$=> (r_{1} + r_{2})^{2} - 2 r_{1} r_{2} = 490$
$=> (28)^{2} - 2 r_{1} r_{2} = 490$
$=> 784 - 2 r_{1} r_{2} = 490$
$=> 2 r_{1} r_{2} = 294$
Now, $(r_{1} - r_{2})^{2} = {r_{1}}^{2} + {r_{2}}^{2} - 2 r_{1} r_{2}$
$=> (r_{1} - r_{2})^{2} = 490 - 294$
$=> (r_{1} - r_{2})^{2} = 196$
$=> (r_{1} - r_{2}) = 14$ cm

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Two circles touch each other externally The sum of their areas is 490 π cm2 Their centers are separated by 28 cm Find the difference of their radii (in cm)

Two circles touch each other externally The sum of their areas is 490 $π$ cm $^{2}$ Their centers are separated by 28 cm Find the difference of their radii (in cm)