The equations of the sides $AB$,$BC$ and $CA$ of a triangle $ABC$ are $2x + y = 0$,$x + py = 39$ and $x - y = 3$ respectively and $P(2, 3)$ is its circumcentre. Then which of the following is $NOT$ true?

If the equation of the base of an equilateral triangle is $x+y=6$ and the opposite vertex is the point $(-1, -1)$,then the area of the triangle is equal to $k$ sq. units. Find the value of $k$.

Let $A(-2,-1)$,$B(1,0)$,$C(\alpha, \beta)$,and $D(\gamma, \delta)$ be the vertices of a parallelogram $ABCD$. If the point $C$ lies on $2x-y=5$ and the point $D$ lies on $3x-2y=6$,then the value of $|\alpha+\beta+\gamma+\delta|$ is equal to . . . . . . .

In an isosceles $\triangle ABC$,the coordinates of vertices $B$ and $C$ of the base $BC$ are $(3, 2)$ and $(2, 3)$ respectively. If the equation of the line $AB$ is $3y = 2x$,then the equation of the line $AC$ is

Let the line $x+y=1$ meet the axes of $x$ and $y$ at $A$ and $B$,respectively. $A$ right-angled triangle $AMN$ is inscribed in the triangle $OAB$,where $O$ is the origin and the points $M$ and $N$ lie on the lines $OB$ and $AB$,respectively. If the area of the triangle $AMN$ is $\frac{4}{9}$ of the area of the triangle $OAB$ and $AN : NB = \lambda : 1$,then the sum of all possible values of $\lambda$ is:

The bisectors of the angles of a parallelogram enclose a