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Two circles of radii 5.5 cm and 4.2 cm touch each other externally. Find the distance between their centres.
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Text Solution
Answer : Distance between the centetes is 9.7 cm.
Solution : Let the radii of the two cercles be `r_(1)" and r_(2)`. <br> `r_(1)=5.5 cm" and " r_(2)=4.2 cm " " "……."(" Given ")` <br> The two circles are touching each other externally. <br> `:.` by theorem of touching circles, the centres and the point of contact are collinear. <br> The distance between the centres of the circles touching externally is equal to the difference of their radii <br> `:.` distance between thir centres <br> `=r_(1)+r_(2)=5.5+4.2=9.7cm`.
Four alternative answers for the following question is given. Choose the correct alternative.
Two circles of radii 5.5 cm and 4.2 cm touch each other externally. Find the distance between their centres
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.
∴ By a theorem of touching circles,
P−Q−R
PR = PQ + QR ...[The distance between the centres of the circles touching externally is equal to the sum of their radii]
= 5.5 + 4.2 = 9.7 cm
∴ The distance between the centres of the circles is 9.7 cm.
Concept: Touching Circles
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