Question

two circles touch internally . the sum of their areas is 170Pi cm^2 and the distance between their centres is 4 cm find the radii of the circles? ​

Answer 1

ANSWER :-

7,11cm is your answer

EXPLANATION

Let radius of circle A be r

1

and radius of circle B be r

2

Given, r

1

−r

2

=4 ---------(i)

and πr

1

2

+πr

2

2

=170π

⇒r

1

2

+r

2

2

=170 -----------(ii)

(i) r

1

=4+r

2

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

⇒(4+r

2

)

2

+r

2

2

=170

⇒16+8r

2

+r

2

2

+r

2

2

=170

⇒2r

2

2

+8r

2

−154=0

⇒2r

2

2

+22r

2

−14r

2

−154=0

⇒2r

2

(r

2

+11)−14(r

2

+11)=0

⇒(r

2

+11)((2r

2

−14))=0

⇒r

2

=−11 (not possible) or r

2

=7

Thus, r

2

=7

r

1

=r

2

+4

⇒r

1

=7+4=11

Thus, the radius of the two circles are 11 cm and 7 cm.

Answer 2

Answer:

11 cm , 7 cm

Step-by-step explanation:

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Two circle touch internally. The sum of there areas is 170 πcm

2

and the distance between their centres is 4 cm. Find the radii of the circles

241975

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Solution

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Correct option is D)

Let radius of circle A be r

1

and radius of circle B be r

2

Given, r

1−r

2=4 ---------(i)

and πr

1

2

+πr

2

2

=170π

⇒r

1

2

+r

2

2

=170 -----------(ii)

(i) r

1

=4+r

2

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

⇒(4+r

2

)

2

+r

2

2

=170

⇒16+8r

2

+r

2

2

+r

2

2

=170

⇒2r

2

2

+8r

2

−154=0

⇒2r

2

2

+22r

2

−14r

2

−154=0

⇒2r

2

(r

2

+11)−14(r

2

+11)=0

⇒(r

2

+11)((2r

2

−14))=0

⇒r

2

=−11 (not possible) or r

2

=7

Thus, r

2

=7

r

1

=r

2

+4

⇒r

1

=7+4=11

Thus, the radius of the two circles are 11 cm and 7 cm.