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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