The triangle formed by joining the points $P(2, 7)$,$Q(4, -1)$,and $R(-2, 6)$ is:

The points $\left( \frac{a}{\sqrt{3}}, a \right)$,$\left( \frac{2a}{\sqrt{3}}, 2a \right)$,and $\left( \frac{a}{\sqrt{3}}, 3a \right)$ are the vertices of:

Two equal sides of an isosceles triangle are given by $7x-y+3=0$ and $x+y-3=0$. If the slope $m$ of the third side is an integer,then $m=$

Let $\alpha, \beta, \gamma, \delta \in \mathbb{Z}$ and let $A(\alpha, \beta), B(1, 0), C(\gamma, \delta)$ and $D(1, 2)$ be the vertices of a parallelogram $ABCD$. If $AB = \sqrt{10}$ and the points $A$ and $C$ lie on the line $3y = 2x + 1$,then $2(\alpha + \beta + \gamma + \delta)$ is equal to

If the circumcenter of the triangle formed by the points $A(a, 3)$,$B(b, 5)$,and $C(a, b)$ is $(1, 1)$,then out of all the possible coordinates of $C$,the sum of the absolute values of the distinct coordinates of $C$ is

The equations of the perpendicular bisectors of the sides $AB$ and $AC$ of $\triangle ABC$ are $x-y+5=0$ and $x+2y=0$ respectively. If the coordinates of $A$ are $(1,-2)$,then the equation of the line $BC$ is