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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

Practice Set 3.2 | Q 2 | Page 58

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.

∴ 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.

Explanation:-

Let there be two circles with centers P and R touching each other externally at point Q. We know that PQ = 5.5 cm and QR = 4.2 cm. By the theorem of touching circles, we have P-Q-R.

The distance between the centers of the circles is equal to the sum of their radii. Therefore, we have PR = PQ + QR. Substituting the given values, we get:

PR = 5.5 + 4.2 = 9.7 cm

Hence, the distance between the centers of the circles is 9.7 cm.

Chapter 3 – Circle – Text Book Solution

Practice set 3.2 | Q 2 | Page 58

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