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

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

The medians of a $\Delta ABC$ are $9 \, cm, 12 \, cm$ and $15 \, cm$ respectively. Then the area of the triangle is.....$sq \, cm$.

The medians $AD$ and $BE$ of a triangle with vertices $A(0, b)$,$B(0, 0)$,and $C(a, 0)$ are perpendicular to each other,if

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

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.)