If $A(4, -3)$,$B(3, -2)$,and $C(2, 8)$ are the vertices of a triangle,then its centroid will be

If the midpoints of the sides of a triangle are $(0, 1)$,$(1, 1)$,and $(1, 0)$,find the $x$-coordinate of its incentre.

The $x-$ coordinate of the incentre of the triangle that has the coordinates of midpoints of its sides as $(0,1), (1,1)$ and $(1,0)$ is

The circumcenter of the triangle formed by the lines $y = x$,$y = 2x$,and $y = 3x + 4$ is

If $P$ is a point equidistant from all the vertices $A(-1, 3)$,$B(3, 5)$,and $C(5, 7)$ of a triangle $ABC$,then $PA=$

Assertion $(A)$: If the centroid and circumcenter of a triangle are known,its orthocenter can be found.
Reason $(R)$: The centroid,orthocenter,and circumcenter of a triangle are collinear.