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?

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

The orthocentre of the triangle formed by the lines $x + y = 1$ and $xy = 0$ is

Let $PS$ be the median of the triangle with vertices $P(2,2)$,$Q(6,-1)$,and $R(7,3)$. The equation of the line passing through $(1,-1)$ and parallel to $PS$ is:

Consider a triangle having vertices $A(-2, 3)$,$B(1, 9)$,and $C(3, 8)$. If a line $L$ passing through the circum-center of triangle $ABC$ bisects line $BC$ and intersects the $y$-axis at point $\left(0, \frac{\alpha}{2}\right)$,then the value of the real number $\alpha$ is $.....$

If $(0, 0)$,$(6, 0)$,and $(6, 8)$ are the vertices of a triangle,what is its incentre?