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

$A(1, -2), B(-2, 3), C(-1, -3)$ are the vertices of a triangle $ABC$. $L_1$ is the perpendicular drawn from $A$ to $BC$ and $L_2$ is the perpendicular bisector of $AB$. If $(l, m)$ is the point of intersection of $L_1$ and $L_2$, then $26m - 3 =$ (in $l$)

What is the distance from the origin to the centroid of the triangle formed by the points $(1, 1)$,$(0, -7)$,and $(-4, 0)$?

Let $PQR$ be an acute-angled triangle in which $PQ < QR$. From the vertex $Q$,draw the altitude $QQ_1$,the angle bisector $QQ_2$,and the median $QQ_3$,with $Q_1, Q_2, Q_3$ lying on $PR$. Then,

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

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