Concentric Circles Problems


 
 
Concept Explanation
 

Concentric Circles Problems

Concentric Circles: The circle which have common centre point and different radius are called concentric circles.

Illustration: Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

Solution: In the figure two concentric circles have their centre at O. The radius of larger circle C_2  is 5 cm and that of the smaller ciircle C_1 is of radius 3cm

PR is a chord to the outer Circle

PR touches the inner circle at Q, So PR is tangent to the inner circle

Rightarrow ;; OQ perp PR                  [ tangent is perpendicular to radius ]

OQ = 3cm   [Radius of inner circle]    and OP = 5cm       [Radius of outer circle] 

Now Delta POQ is a right angled at Q

OP^2= OQ^2+ PQ^2         [ By pythagorous theorem]

PQ^2= OP^2-OQ^2= 5^2-3^2= 25-16 = 4^2

PQ = 4 cm

PR is a chord  to outer circle and as PR perp OQ, Therefore OQ bisects the chord

PR = 2 X PQ = 2 X 4 = 8 cm

Sample Questions
(More Questions for each concept available in Login)
Question : 1

The figure shows two concentric circles and AD is a chord of larger circle. If the length of AP = 10 cm and BP = 3cm.  Find the value of 3CD + 2AP

 

Right Option : A
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Explanation
Question : 2

The figure shows two concentric circles and AD is a chord of larger circle. If the length of AB = 3 cm. Find the value of CD.

 

Right Option : B
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Explanation
Question : 3

The figure shows two concentric circles and AD is a chord of larger circle. If the length of AP = 10 cm and BP = 3cm.  Find the value of CD.

 

Right Option : D
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Explanation
 
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