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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

  1. \\frac{π}{3})
  2. 1
  3. \\frac{1}{\sqrt{2}})
  4. \\sqrt{2})

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Explanatory Answer



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 = 42 + (4 - r)2
16 + r2 + 8r = 16 + 16 + r2 - 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"

Hence, the answer is 1

Choice B is the correct answer.

 

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