Question

TWO CIRCLES TOUCH INTERNALLY. THE SUM OF THEIR AREAS IS 116πcm^2 AND DISTANCE BETWEEN THEIR CENTERS IS 6cm. FIND THE radii OF THE CIRCLES.
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Answer 1

Step-by-step explanation:

it will help you to understand

Answer 2

Answer:

Correct option is

B

4cm & 10cm.

Given−

Twocirclestouchinternally.

Thedistancebetweentheircertres=6cm.

Theradiioftheouter&innercirclesarer

2

&r

1

respectively.

Thesumoftheirareas=116π.

Tofindout−

(r

2

&r

1

)=?

Solution−

Sincethecirclestouchinternally,

thedistancebetweentheircertres

=thedifferencecebetweentheirradii=6cm.

∴r

2

−r

1

=6cm⟹r

2

=r

1

+6.

Soar.outercircle=π×(r

2

)

2

=π×(r

1

+6)

2

.

Andar.innercircle=π×(r

1

)

2

.

∴Thesumoftheirareas=π×(r

1

+6)

2

+π×(r

1

)

2

=116π.

⟹(r

1

)

2

+6r−40=0

⟹(r

1

+10)(r

1

−4)=0

⟹r

1

=(−10,4)cm.

Werejectthenegativevalueofr

1

sincer

1

isalength.

∴r

1

=4cm.

Sor

2

=(r

1

+6)cm=(4+6)cm=10cm.

∴r

1

=4cm,r

2

=10cm.