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

If the vertices of a triangle are $(0,0)$,$(6,0)$,and $(6,8)$,then its incentre will be:

In a 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 area of $\Delta ABC$ (in sq. units) is

The circumcentre of the triangle formed by the points $A(1, \sqrt{3})$,$B(-1, -\sqrt{3})$,and $C(3, -\sqrt{3})$ is

Consider a $\triangle PQR$ in which the relation $QR^2 + PR^2 = 5PQ^2$ holds. Let $G$ be the point of intersection of medians $PM$ and $QN$. Then,$\angle QGM$ is always

If the orthocentre of the triangle,whose vertices are $(1,2), (2,3)$ and $(3,1)$ is $(\alpha, \beta)$,then the quadratic equation whose roots are $\alpha+4\beta$ and $4\alpha+\beta$ is: