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  • Radii of the smallest and the largest circle passing through a point lying on the sides of a rectangle with vertices <img alt="\mathrm{( \pm 2, \pm 1)}" src="https://entrancecorner.oncodecogs.com/g

Radii of the smallest and the largest circle passing through a point lying on the sides of a rectangle with vertices \mathrm{( \pm 2, \pm 1)} and touching the circle \mathrm{ x^2+y^2=9, are\: r_1 \: and\: r_2 } respectively. Let \mathrm{ d=\left|r_1-r_2\right| } then minimum value of \mathrm{ d } is

Option: 1

\frac{1}{2}


Option: 2

1


Option: 3

2


Option: 4

3


Answers (1)

best_answer

\begin{aligned} & x+2 r_1=r \\ & 2 r_2-x=r \\ & \left|r_1-r_2\right|=x \\ & \Rightarrow\left|r_1-r_2\right| \text { is minimum } \\ & \text { When x is minimum. } \\ & \left|r_1-r_2\right|=1 \end{aligned}
 

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shivangi.shekhar

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