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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. $\sqrt{2}$ 🚀 Introductory Offer! Buy CAT'21 95-99 Booster Course for just Rs. 4500 Valid until 19th Sep 2IIM : Best Online CAT Coaching. Video Explanation Best CAT Coaching in Chennai CAT Coaching in Chennai - CAT 2021Online Batches Available Now! 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"

Choice B is the correct answer.

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