The centroid of the triangle $ABC$,where $A \equiv (2,3)$,$B \equiv (8,10)$,and $C \equiv (5,5)$ is

If $O, G, S$ are respectively the orthocentre,centroid and circumcentre of a triangle whose vertices are $A(2,3), B(2,4)$ and $C(4,3)$,then $AO^2 + 9BG^2 + 4CS^2 =$

What is the orthocenter of the triangle with vertices $(2, \frac{\sqrt{3}-1}{2})$,$(\frac{1}{2}, -\frac{1}{2})$,and $(2, -\frac{1}{2})$?

Find the orthocenter of the triangle with vertices $(8, -2)$,$(2, -2)$,and $(8, 6)$.

If in triangle $ABC$,$A \equiv (1, 10)$,circumcentre $\equiv \left( -\frac{1}{3}, \frac{2}{3} \right)$ and orthocentre $\equiv \left( \frac{11}{3}, \frac{4}{3} \right)$,then the coordinates of the mid-point of the side opposite to $A$ are:

The quadratic equation whose roots are the coordinates of the circumcentre of the triangle formed by the points $(-2,-1), (6,-1),$ and $(2,5)$ is