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Question
Two circles of radii 5.5 cm and 4.2 cm touch each other externally. Find the distance between their centres.
Solution
Let the two circles having centres P and R touch each other externally at point Q.
Here, PQ = 5.5 cm, QR = 4.2 cm
The two circles touch each other externally. ...(P−Q−R)
If the circles touch each other externally, distance between their centres is equal to the sum of their radii.
∴ By theorem of touching circles,
∴ PR = PQ + QR
∴ PR = 5.5 + 4.2
∴ PR = 9.7 cm
∴ The distance between the centres of the circles is 9.7 cm.
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