If $P(2, 2)$,$Q(-2, 4)$,and $R(3, 4)$ are the vertices of $\triangle PQR$,then the equation of the median through vertex $R$ is $........$

In $\triangle ABC$,the coordinates of $A$ are $(1, 2)$ and the equations of the medians through $B$ and $C$ are $x+y=5$ and $x=4$ respectively. Then the midpoint of $BC$ is

The circumcentre of the triangle formed by the points $A(1, \sqrt{3})$,$B(-1, -\sqrt{3})$,and $C(3, -\sqrt{3})$ is

The circumcentre of the triangle with vertices $(-2, 3)$,$(2, -1)$,and $(4, 0)$ is:

The incentre of the triangle with vertices $(1, \sqrt{3}), (0, 0)$ and $(2, 0)$ 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: