If O is the origin and OP, OQ are distinct tangents to the circle x2+y2+2gx+2fy+c=0, the circumcentre of the triangle OPQ is
None of these
Since PQ is the chord of contact of the tangents from the origin O to the circle
x2+y2+2gx+2fy+c=0,---------------(1)
equation of PQ is
gx+fy+c=0---------------------------------- (2)
An equation of a circle through the intersection of (1) and (2) is given by
x2+y2+2gx+2fy+c+λ(gx+fy+c)=0 -----------(3)
If the circle (3) passes through O, the origin, then c+λc=0, i.e., λ=−1, and the equation of the circle (3) becomes
x2+y2+gx+fy=0
Centre of this circle is (-g/2, -f/2), and hence it is the circum centre of the triangle OPQ.