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

Two vertices of a triangle $ABC$ are $A(3, -1)$ and $B(-2, 3)$,and its orthocentre is $P(1, 1)$. If the coordinates of the point $C$ are $(\alpha, \beta)$ and the centre of the circle circumscribing the triangle $PAB$ is $(h, k)$,then the value of $(\alpha + \beta) + 2(h + k)$ equals :

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

The incentre of the triangle formed by the straight lines $y=\sqrt{3}x$,$y=-\sqrt{3}x$ and $y=3$ is

The orthocenter of the triangle formed by the lines $4x - 7y + 10 = 0$,$x + y - 5 = 0$,and $7x + 4y - 15 = 0$ is:

The circumcentre of a triangle formed by the lines $xy + 2x + 2y + 4 = 0$ and $x + y + 2 = 0$ is