If the middle point of a chord of the circle $x^{2} + y^{2} + x - y - 1 = 0$ be (1,1), then the length of the chord is

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5/2

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Solution

The correct option is D
5/2

Here radius of circle is

$A C = \sqrt{(\frac{1}{2})^{2} + (\frac{1}{2})^{2} + 1} = \sqrt{\frac{3}{2}}$

and $C B = \sqrt{(0)^{2} + {(\frac{1}{2})}^{2}} = (\frac{1}{2})$

Now $A B^{2} = A C^{2} - B C^{2} = \frac{3}{2} - \frac{1}{4} = \frac{5}{4}$

$∴ l e n g t h o f c h o r d i s \frac{5}{2}$

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