Let the orthocentre and centroid of a triangle be $A(-3, 5)$ and $B(3, 3)$ respectively. If $C$ is the circumcentre of this triangle,then the radius of the circle having line segment $AC$ as diameter is:

Two vertices of a triangle $ABC$ are $A(3, -1)$ and $B(-2, 3)$,and its orthocentre is $P(1, 1)$. If the coordinates of the point $C$ are $(\alpha, \beta)$ and the centre of the circle circumscribing the triangle $PAB$ is $(h, k)$,then the value of $(\alpha + \beta) + 2(h + k)$ equals :

Let $A(0,0), B(3,0), C(0,-4)$ be the vertices of $\triangle ABC$. Then the coordinates of the incentre of $\triangle ABC$ are:

Find the orthocenter of the triangle whose vertices are $(0, 0), (2, -1),$ and $(1, 3).$

If the orthocentre of the triangle formed by the lines $2x+3y-1=0$,$x+2y-1=0$,and $ax+by-1=0$ is the centroid of another triangle,whose circumcentre and orthocentre are $(3,4)$ and $(-6,-8)$ respectively,then the value of $|a-b|$ is..........

If $P(6,1)$ is the orthocentre of the triangle whose vertices are $A(5,-2)$,$B(8,3)$,and $C(h, k)$,then the point $C$ lies on the circle: