If the coordinates of the orthocenter and the centroid of a triangle are $(4, -1)$ and $(2, 1)$ respectively,then what are the coordinates of the circumcenter of the triangle?

If $(a, b - c)$,$(b, c - a)$,and $(c, a - b)$ are the vertices of a triangle,then where does the centroid of the triangle lie?

If the coordinates of the midpoints of the sides of a triangle are $(4, 2), (3, 3)$ and $(2, 2)$,what are the coordinates of the centroid?

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

Two vertices of a triangle are $(5, -1)$ and $(-2, 3)$. If the orthocentre is the origin,then the coordinates of the third vertex are:

If the equations of the perpendicular bisectors of the sides $AB$ and $AC$ of a $\triangle ABC$ are $x-y+5=0$ and $x+2y=0$ respectively,and if $A$ is $(1,-2)$,then the equation of the perpendicular bisector of the side $BC$ is