Assertion (A): Two circles touch internally. The sum of their areas is 116\pi\mathrm{\ }cm2and the distance between their centres is 6 cm. Then, radii of the circles are 4 cm and 10 cm. Reason (R): When two circles

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Solution

Q.
Assertion (A): Two circles touch internally. The sum of their areas is $116 π c m^{2}$ and the distance between their centres is 6 cm. Then, radii of the circles are 4 cm and 10 cm.

Reason (R): When two circles touch internally, then difference of their radii is equal to distance between their centres.

1 Both A and R are true, and R is the correct explanation of A.

2 Both A and R are true, but R is not the correct explanation of A

3 A is true, but R is false.

4 A is false, but R is true.

Ans.
(1)

Let two circles having centres $O_{1}, O_{2} a n d r a d i i r_{1}, r_{2}$ touch internally at point P .

$∴ S u m o f t h e i r a r e a s = 116 π c m^{2} π r_{1}^{2} + π r_{2}^{2} = 116 π \Rightarrow r_{1}^{2} + r_{2}^{2} = 116 . . . (i) A l s o, r_{1} - r_{2} = 6 . . . (ii) T h e v a l u e s r_{1} = 10 cm a n d r_{2} = 4 cm s a t i s f y b o t h e q u a t i o n s (i) a n d (i i) .$

∴ Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

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