Geometry: Concentric Circles
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Concentric Circles

Circles having the same centre but with different radii are said to be concentric circles.

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Example: Two concentric circles with centre O have P, Q, R, S as the points of intersection with the line I as shown in Fig. below. If PS = 14 cm and QR = 10 cm, find the lengths of PQ, RS, PR and QS.
 Solution: As OM QR
Therefore, QM = RM =1/2QR =5 cm
 Similarly, OM PS
PM = SM = 1/2PS = 7 cm.

Now, PQ = PM - QM = (7 - 5) = 2cm.
Also, RS = SM - RM = (7 - 5) = 2cm.

Therefore,
PR = PQ + QR = (2 + 10)cm = 12 cm
and QS = QR + RS =(10 + 2)cm = 12 cm.

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