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CAT 2019 Slot 2 — QA Question 7

2 CirclesEasy

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

Answer & solution

  • A

    π/3

  • 1

  • C

    1/√2

  • D

    √2

Solution

Let the radius of the third circle be ‘x’ cm.

AF = DE = 4 cm ⇒ AK = DC = (4 – x) cm
 
In ∆ADC, AC2 = AD2 + DC2.
 
(4 + x)2 = 42 + (4 – x)2
 
∴ x = 1.
 
Hence, option (a).

CAT 2019 Slot 2 QA Q7: Two circles, each of radius 4 cm, touch externally. Each of these two circles is touched externally by a third — Solution | TheCATExam