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There are two circles intersecting each other. Another smaller

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There are two circles intersecting each other. Another smaller circle with centre O is lying between the common regions of two larger circles. Centres of the circle (i.e., A, O and B) are lying on a straight line. If AB = 16 cm and the radii of the larger circles are 10 cm each, what is the area of the smaller circle?

4 π c

2

2 π c

2

4

c

2

π

c

m\displaystyle{2}

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There are two circles intersecting each other. Another smaller circle with centre O is lying between the common regions of two larger circles. Centres of the circle (i.e., A, O and B) are lying on a straight line. If AB = 16 cm and the radii of the larger circles are 10 cm each, what is the area of the smaller circle?

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Text solutionVerified

(a):

A B = 16 c m

A Q = 10 c m

and

A O =

2

=8cm

OQ=AQ−AO⇒10−8=2cm

O Q (= O P) i s t h e r a d i u s o f t h e s m a l \leq r e n c l o s e d \circ \leq b e t w e e n t w o a r c s . A r e a o f \circ \leq w i t h c e n t r e O i s

π×

(2)

= 4 π c

2

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Question Text	There are two circles intersecting each other. Another smaller circle with centre O is lying between the common regions of two larger circles. Centres of the circle (i.e., A, O and B) are lying on a straight line. If AB = 16 cm and the radii of the larger circles are 10 cm each, what is the area of the smaller circle?
Answer Type	Text solution:1
Upvotes	150

Text solutionVerified

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