The length of the tangent from (x1, y1) to the circle x2 + y2 + 2gx + 2fy + c = 0, is
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(x12 + y12 + 2gx1 + 2fy1 + c)
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(x12 + y12)1/2
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[(x1 + g)2 + (y1 + f)2]1/2
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None of these
The length of the tangent from a point (x1, y1) to a circle x^2 + y^2 + 2gx + 2fy + c = 0 is given by the square root of the power of the point, which is sqrt(x1^2 + y1^2 + 2gx1 + 2fy1 + c). Option A lacks the square root, and other options are incorrect.
The standard formula for the length of a tangent from an external point (x1, y1) to a circle is the square root of (x1 squared plus y1 squared plus 2gx1 plus 2fy1 plus c). Option A is missing the square root over the entire expression, Option B omits the linear and constant terms, and Option C represents the distance from the external point to the center of the circle. Therefore, the correct formula is not listed, making the answer None of these.