Question

Two circles touch externally. the sum of their areas is 58π cm square and the distance between their centres is 10cm. find the radii of the two circles.




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Answer 1

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Answer 2

Answer:

7 cm and 3 cm

Step-by-step explanation:

Let x cm be the radii of circle A ( in fig)

Then the radii of circle B is (10 - x) cm

the area of circle A = π$x^{2}$ cm²

the area of circle B = π(10 - x)² cm²

According to question,

πx² + π(10 - x)² = 58π

or, π{ x² + (10-x)²} = 58π ( dividing both side by π)

or, $x^{2} +(10-x)^{2} = 58$

or, $x^{2} + 10^{2} - 20x +x^{2} =58$

or, $2x^{2} - 20x + 100 - 58 =0$

or, $2x^{2} -20x + 42=0$ ( dividing both sides by 2)

or,$x^{2} -10x+21=0$

Using Sridhar Acharya's rule we get,

$x=\frac{-(-10)\±\sqrt{10^{2}- (4*1*21)} }{2*1}$

or, $x=\frac{10\± 4 }{2}$

or x = 7 cm , x = 3 cm

So, the radii of circle A is 7 cm or 3 cm

and the radii of circle B is 3cm or 7cm.

see the fig in the attachment