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There are two circles \mathrm{C_1} and \mathrm{C_2} touching the coordinate axes, also touch each other externally, if \mathrm{C_1} is smaller than \mathrm{C_2}. The radius of \mathrm{C_1} is 2 units and the radius of  \mathrm{C_2} is \mathrm{6+\lambda \sqrt{2} \ . Then \ \lambda} is equal to

Option: 1

4


Option: 2

3


Option: 3

2


Option: 4

1


Answers (1)

best_answer

From the figure, we observe that OQ = OR + RQ

\mathrm{\begin{array}{ll} \Rightarrow & \sqrt{2} r=O P+P R+R Q \\ \Rightarrow & \sqrt{2} r=2 \sqrt{2}+2+r \\ \Rightarrow & r=2\left(\frac{\sqrt{2}+1}{\sqrt{2}-1}\right)=2(3+2 \sqrt{2})=6+4 \sqrt{2} \end{array}}

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Suraj Bhandari

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