A square is inscribed inthe circle

Question:

A square is inscribed inthe circle 

$x^{2}+y^{2}-6 x+8 y-103=0$ with its sides parallel to the corrdinate axes. Then the distance of the vertex of this square which is nearest to the origin is :-

  1. 13

  2. $\sqrt{137}$

  3. 6

  4. $\sqrt{41}$


Correct Option: , 4

Solution:

$\mathrm{R}=\sqrt{9+16+103}=8 \sqrt{2}$

$\mathrm{OA}=13$

$\mathrm{OB}=\sqrt{265}$

$\mathrm{OC}=\sqrt{137}$

$\mathrm{OD}=\sqrt{41}$

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