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 vertices of a triangle are $(6,0), (0,6)$ and $(6,6)$. The distance between its circumcentre and centroid is

Let the area of a $\triangle PQR$ with vertices $P(5, 4)$,$Q(-2, 4)$,and $R(a, b)$ be $35$ square units. If its orthocenter and centroid are $O\left(2, \frac{14}{5}\right)$ and $C(c, d)$ respectively,then $c+2d$ is equal to:

The orthocentre of the triangle with vertices $(-2, -6)$,$(-2, 4)$ and $(1, 3)$ is

The vertices of a triangle are $A(4, -2)$,$B(2, 3)$,and $C(5, -4)$. Find the equation of the median drawn from $C$.

In $\triangle ABC$, the coordinates of $A$ are $(1, 2)$ and the equations of the medians through $B$ and $C$ are $x+y=5$ and $x=4$ respectively. Then the midpoint of $BC$ is