If the straight line $y = mx + c$ touches the circle ${x^2} + {y^2} - 4y = 0$, then the value of $c$ will be

  • A

    $1 + \sqrt {1 + {m^2}} $

  • B

    $1 - \sqrt {{m^2} + 1} $

  • C

    $2(1 + \sqrt {1 + {m^2}} )$

  • D

    $2 + \sqrt {1 + {m^2}} $

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