The points $(0, 8/3)$,$(1, 3)$ and $(82, 30)$ are the vertices of

In an equilateral triangle $PQR$,let the vertex $P$ be at $(3, 5)$ and the side $QR$ be along the line $x + y = 4$. If the orthocentre of the triangle $PQR$ is $(\alpha, \beta)$,then $9(\alpha + \beta)$ is equal to:

Suppose $\triangle ABC$ is an isosceles triangle with $\angle C=90^{\circ}$,$A=(2,3)$ and $B=(4,5)$. Then the centroid of the triangle is

If $(4,3)$ and $(1,-2)$ are the end points of a diagonal of a square,then the equation of one of its sides is

The area of the parallelogram formed by the lines $x \cos \alpha + y \sin \alpha = p$,$x \cos \alpha + y \sin \alpha = q$,$x \cos \beta + y \sin \beta = r$,and $x \cos \beta + y \sin \beta = s$ is:

The sides of a triangle are $x = 2$,$y + 1 = 0$,and $x + 2y = 4$. Find its circumcenter.