Question

Two circles touch externally. The sum of their areas is 117π cm² and the distance between their centres is 15 cm. Find the radii of the two circles.​

Answer 1

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Two circles touch externally. The sum of their areas is 117 πcm

2

and the distance between their centres is 15 cm. Find the radii of the two circles.

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Solution

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Correct option is A)

Let radius of circle A be r

1

and radius of circle B be r

2

Given, r

1

+r

2

=15 -------(i)

and πr

1

2

+πr

2

2

=117π

⇒r

1

2

+r

2

2

=117 ------(ii)

(i)⇒r

1

+r

2

=15

⇒r

1

=15−r

2

Now, putting this value in (ii), we get

⇒(15−r

2

)

2

+r

2

2

=117

⇒15

2

−2×15×r

2

+r

2

2

+r

2

2

=117

⇒225−30r

2

+2r

2

2

=117

⇒2r

2

2

−30r

2

+108=0

⇒2r

2

2

−18r

2

−12r

2

+108=0

⇒2r

2

(r

2

−9)−12(r

2

−9)=0

⇒(r

2

−9)(2r

2

−12)=0

⇒r

2

=9 or r

2

=

2

12

=6

⇒r

1

=15−9 or r

1

=15−6

⇒r

1

=6 or r

1

=9

⇒r

1

>r

2

Thus, the radius of the two circles are 9 cm and 6 cm.