Find the point on the $X$-axis which is equidistant from $(5, 4)$ and $(-2, 3)$.

$\overline{AB}$ 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 $\dots$.

Find the ratio in which the point $P \left(\frac{3}{4}, \frac{5}{12}\right)$ divides the line segment joining the points $A \left(\frac{1}{2}, \frac{3}{2}\right)$ and $B(2, -5)$. (in $: 5$)

The segment joining $A (-2, 1)$ and $B (7, 8)$ is divided into five congruent segments. Find the coordinates of the third point from $A$.

In which ratio does the point $P (-4, 3)$ divide the line segment joining the points $A (1, -2)$ and $B (-6, 5)$?

State whether the following statement is true or false. Justify your answer.
$A$ circle has its centre at the origin and a point $P(5,0)$ lies on it. The point $Q(6,8)$ lies outside the circle.