Distance between two external touching circles with radii 2cm and 2.5 cm is_

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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.

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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Text Solution

2 cm `2.5` cm `1.5` cm 8 cm

Solution : Let two circles with centres O and O' touch each other externally at the point C. The radius of the first circle is `5 cm therefore OC= 5cm,` and the radius of the second circle is 3 am, `therefore O'C=3cm.` <br> Now the distance between the centres of the circeles `=OO'= OC+CO' =5 cm +3 cm =8 cm` <br> `therefore `(d) is correct <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/CBH_MAT_X_SOG_C04_SLV_016_S01.png" width="80%">

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