Chord of contacts

Circles of Class 11

Chord of Contact

If the circle is x2 + y2 + 2gx + 2fy + c = 0

and if tangents have been drawn from an external point A(x1, y1) touching the circle at B and C then the equation of BC (chord of contact) is T = 0 and is written as,

xx1 + yy1 + g(x + x1) + f(y + y1) + c = 0

Length of the tangent in the general case from a point (x1, y1)

=

Orthogonality of two circles is given by

S1 = x2 + y2 + 2g1x + 2f1y + c1

and S2 = x2 + y2 + 2g2x + 2f2y + c2

the condition 2g1g2 + 2f1f2 = c1 + c2

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