Let $A(-3, 2)$ and $B(-2, 1)$ be the vertices of a triangle $ABC$. If the centroid of this triangle lies on the line $3x + 4y + 2 = 0$,then the vertex $C$ lies on the line

The vertices of a triangle are $A(0,0), B(0,2)$ and $C(2,0)$. Find the distance between its orthocentre and circumcentre.

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

$A$ tower stands vertically inside an acute-angled triangular park $\Delta PQR$. If the angle of elevation of the top of the tower from each corner of the park is the same,then in $\Delta PQR$,the foot of the tower is at the

Let $ABC$ be an equilateral triangle with orthocenter at the origin and the side $BC$ on the line $x+2\sqrt{2}y=4$. If the coordinates of the vertex $A$ are $(\alpha, \beta)$, then the greatest integer less than or equal to $|\alpha+\sqrt{2}\beta|$ is

The orthocentre of the triangle formed by lines $x+y+1=0$,$x-y-1=0$,and $3x+4y+5=0$ is