If the coordinates of the midpoints of the sides of a triangle are $(4, 2), (3, 3)$ and $(2, 2)$,what are the coordinates of the centroid?

Find the orthocenter of the triangle with vertices $(8, -2)$,$(2, -2)$,and $(8, 6)$.

If the vertices $P, Q, R$ of a triangle $PQR$ are rational points,which of the following points of the triangle $PQR$ is (are) always a rational point $(s)$? ($A$ rational point is a point both of whose coordinates are rational numbers.)

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

Let $A(1,0), B(6,2)$ and $C(\frac{3}{2}, 6)$ be the vertices of a triangle $ABC$. If $P$ is a point inside the triangle $ABC$ such that the triangles $APC, APB$ and $BPC$ have equal areas,then the length of the line segment $PQ,$ where $Q$ is the point $(-\frac{7}{6}, -\frac{1}{3})$ is

The incentre of the triangle formed by the vertices $(0, 0)$,$(5, 12)$,and $(16, 12)$ is: