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CAT 2019 Quant Question with Solution 40

Question:
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. $\sqrt{2}$
  2. $\pi / 3$
  3. $1 / \sqrt{2}$
  4. 1
Show Answer

Correct Answer: Option: 4

Refer to the figure

SO=4-r.

Applying Pythagoras theorem in triangle POS, we get

${{\left( 4+r \right)}^{2}}={{4}^{2}}+{{\left( 4-r \right)}^{2}}$

$\Rightarrow {{\left( 4+r \right)}^{2}}-{{\left( 4-r \right)}^{2}}=16$

$\Rightarrow 4\times 4\times r=16$

$\Rightarrow r=1$


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