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

Let $A(1,0), B(6,2)$ and $C(\frac{3}{2}, 6)$ be the vertices of a triangle $ABC$. If $P$ is a point inside the triangle $ABC$ such that the triangles $APC, APB$ and $BPC$ have equal areas,then the length of the line segment $PQ,$ where $Q$ is the point $(-\frac{7}{6}, -\frac{1}{3})$ is

The two vertices of a triangle are $(-1, 4)$ and $(5, 2)$. If its centroid is $(0, -3)$,find the third vertex.

If $(\alpha, \beta)$ is the orthocentre of the triangle with the vertices $(2,2), (5,1), (4,4)$,then $\alpha+\beta=$

What is the orthocentre of the triangle formed by the lines $xy = 0$ and $x + y = 1$?

The coordinates of the orthocentre of the triangle bounded by the lines $4x - 7y + 10 = 0$,$x + y = 5$,and $7x + 4y = 15$ are: