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

Slot – 2 – Quantitative Aptitude – Geometry – Circles – Two circles, each of radius 4 cm

Q. 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

Answer: 1

Solution: 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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