Two vertices of a triangle are $(5, 4)$ and $(-2, 4)$. If its centroid is $(5, 6)$,then the third vertex has the coordinates:

Let $A \equiv (4,4), B \equiv (8,4), C \equiv (4,8)$. If $P, Q, R$ are the midpoints of sides $AB, BC, CA$ respectively and $(\alpha, \beta)$ are the coordinates of the orthocentre of $\Delta PQR$,then the value of $\alpha + \beta$ is

Let $ABC$ be an equilateral triangle with orthocenter at the origin and the side $BC$ on the line $x+2\sqrt{2}y=4$. If the coordinates of the vertex $A$ are $(\alpha, \beta)$,then the greatest integer less than or equal to $|\alpha+\sqrt{2}\beta|$ is

If the coordinates of the vertices of triangle $ABC$ are $(6, 0)$,$(0, 6)$,and $(7, 7)$ respectively,find the circumcenter of the triangle.

The coordinates of the orthocentre of the triangle with vertices $A(0, 0)$,$B(3, 4)$,and $C(4, 0)$ are:

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