Name the type of triangle $PQR$ formed by the points $P(\sqrt{2}, \sqrt{2})$,$Q(-\sqrt{2}, -\sqrt{2})$,and $R(-\sqrt{6}, \sqrt{6})$.

The distance of the point $P(-6, 8)$ from the origin is

$\overline{AB}$ is given and $P$ is a point such that $A-P-B$. If $P$ divides $\overline{AB}$ from $A$ in ratio $2:3$,then $P$ divides $\overline{AB}$ from $B$ in ratio $\dots$.

State whether the following statement is true or false. Justify your answer.
$\triangle ABC$ with vertices $A(-2, 0), B(2, 0)$ and $C(0, 2)$ is similar to $\triangle DEF$ with vertices $D(-4, 0), E(4, 0)$ and $F(0, 4)$.

State whether the following statement is true or false. Justify your answer.
The point $A (2,7)$ lies on the perpendicular bisector of the line segment joining the points $P (6,5)$ and $Q (0,-4)$.

If the circumcentre of the triangle with vertices $(a, -1)$,$(6, -9)$,and $(10, b)$ is $(6, -5)$,then find the values of $a$ and $b$.