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Parin Sir > Quantitative Aptitude (Maths) > Co–Ordinate Geometry > Circle > Length of  a Tangent > Length of  a Tangent

Length of  a Tangent

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☼ Length of  a Tangent :–

 Two tangents to a circle can be drawn from a point lying in the exterior of the circle.

In this case,

  • PT1 =   PT2
  • PC bisects  \overline{T_1T_2} at  right

 If

 (i) circle is   S : x2 +  y2 =   r2, then  the length  of   a   tangent  from  the  point   P( x1, y1 )   is   PT1  =   PT2  =  \sqrt{x_1^2+y_1^2-r^2}

 (ii) circle is   S : x2 + y2 + 2gx + 2fy + c = 0, then  the length  of   a   tangent  from  the  point   P( x1, y1 )   is   PT1  =   PT2 =  \sqrt{x_1^2+y_1^2+2\mathrm{g} \mathrm{x}_1+2\mathrm{f} \mathrm{y}_1+c}

 

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