The vertices of a triangle are $A(0,0), B(0,2)$ and $C(2,0)$. Find the distance between its orthocentre and circumcentre.

If the vertices of a triangle are $(2, 1), (5, 2)$ and $(3, 4)$,then its circumcentre 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

Let the vertex of a triangle $ABC$ be $A(1, 2)$, and the mid-point of the side $AB$ be $M(5, -1)$. If the centroid of this triangle is $G(3, 4)$ and its circumcenter is $O(\alpha, \beta)$, then $21(\alpha + \beta)$ is equal to:

If the median $AD$ of the triangle $ABC$ is bisected at $E$ and $BE$ meets $AC$ in $F$,then $AF: AC=$

The vertices of a triangle are $A(4, -2)$,$B(2, 3)$,and $C(5, -4)$. Find the equation of the median drawn from $C$.