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Two circles, each of radius 4 cm | Quantitative Aptitude - Geometry – Circles

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The question below is from previous year CAT question from CAT 2019 exam comes from CAT Circles : Two circles, each of radius 4 cm

Find out by answering this question which tests an aspirant’s Quantitative Ability Skills.

You may also find remaining question solution of CAT 2019, Slot 2 by searching the question in the search bar.

CAT 2019 - Slot 2 - Quantitative Aptitude - Circles - Question 1 - Two circles, each of radius 4 cm

Q. 1: 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. π/3

2. 1/√2

3. √2

4. 1

 See the figure,

 

In above figure , AD=BD =4 , let radius of 3rd circle = r

 

So AC = 4+r, CD = 4-r

 

Using Pythagoras theorem in right angled triangle ADC,

 

AC^2 = AD^2 + CD^2

 

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

 

16+ r^2 + 8r = 16 + 16 + r^2 – 8r

 

16r = 16

 

r =1

 

 

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