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Question 7 : Two circles, each of radius 4 cm, touch externally. Each of these two circles is touched externally by a third circle. If these three circles have a common tangent, then the radius of the third circle, in cm, is

- \\frac{π}{3})
- 1
- \\frac{1}{\sqrt{2}})
- \\sqrt{2})

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For three circles to have a common tangent, the third circle must lie in between the two circles. Let the radius of the third circle be r cms

Now, Connect the centres of the circles with one another and with the intersection points. Let them be A,B,C,D,E respectively.

Now, from observing the constructed diagram, we find

AB = 8cms

AC = (4 + r) cms

BC = (4 + r) cms

OC = (4 - r) cms

Now, consider the right triangle OBC,

Applying Pythagoras theorem,

(4+r)^{2} = 4^{2} + (4 - r)^{2}

16 + r^{2} + 8r = 16 + 16 + r^{2} - 8r

16r = 16

r = 1 cms

The question is **"Two circles, each of radius 4 cm, touch externally. Each of these two circles is touched externally by a third circle. If these three circles have a common tangent, then the radius of the third circle, in cm, is" **

**Choice B** is the correct answer.

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