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
- $\sqrt{2}$
- $\pi / 3$
- $1 / \sqrt{2}$
- 1
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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