Question

If $O$ is the origin and $OP$ , $OQ$ are distinct tangents to the circle $x^2+y^2+2gx+2fy+c=0,$ then the circumcentre of the triangle $OPQ$ is

• A. $\left(-g,-f\right)$
• B. $\left(g,f\right)$
• C. $\left(-f,-g\right)$
• D. None of these

Answer 1

Answer: (D)

Tangents drawn from the point $O$ , meet the cirle at $P$ & $Q$ and $C$ be the centre of given circle. Then points $O,P,C$ and $Q$ are concyclic. That means any circle passing through $O,P$ and $Q$ also passes through $C$ and $OC$ is the diameter for this circle. Hence mid point of $OC$ is the circumcentre of triangle $OPQ$ .


Coordinates of circumcenter $=\left(\frac{-g}{2},\frac{-f}{2}\right)$