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     EduGorilla 
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    The line (x + g) cos θ + (y + f) sin θ = 1 touches the circle x2 + y2 +  2 gx + 2 fy + c = 0, only if

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    1. g2 + f2 = c + k2
    2. g2 + f2 = c2 + k2
    3. g2 + f2 = c - k2
    4. g2 + f2 = c2 - k2
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