Find the equation of the right bisector of the line segment joining the points $(3, 4)$ and $(-1, 2).$

The length of the perpendicular from the origin,on the normal to the curve $x^{2}+2xy-3y^{2}=0$ at the point $(2,2)$ is

If the image of $\left(\frac{-7}{5}, \frac{-6}{5}\right)$ in a line is $(1, 2)$,then the equation of the line is

Let $P$ be a point inside a $\triangle ABC$ with $\angle ABC = 90^{\circ}$. Let $P_1$ and $P_2$ be the images of $P$ under reflection in $AB$ and $BC$ respectively. The distance between the circumcenters of $\triangle ABC$ and $\triangle P_1PP_2$ is

The equation of the line perpendicular to the line $ax + by + c = 0$ and passing through $(a, b)$ is:

$y-x=0$ is the equation of a side of a triangle $ABC$. The orthocentre and circumcentre of the triangle $ABC$ are respectively $(5,8)$ and $(2,3)$. The reflection of the orthocentre with respect to any side of the triangle lies on its circumcircle. Then the radius of the circumcircle of the triangle is