Point $A$ lies in the exterior of $\odot(P, 10)$. $A$ line from $A$ touches the circle at $B$. If $PA = 26$,then find the length of $AB$.

In the figure,the common tangents $AB$ and $CD$ to two circles with centers $O$ and $O^{\prime}$ intersect at $E$. Prove that the points $O, E, O^{\prime}$ are collinear.

$\overline{PA}$ is a tangent to $\odot(O, r)$ drawn from a point $P$ outside a circle. If $OP = 10$ and $AP = 8$,then the diameter of the circle is equal to $\ldots \ldots \ldots \ldots .$

Write 'True' or 'False' and give reasons for your answer.
If a number of circles touch a given line segment $PQ$ at a point $A$,then their centres lie on the perpendicular bisector of $PQ$.

In the following figure,if $AB = 10$,then $AC = \ldots$

$A$ tangent $\overline{PM}$ is drawn from a point $P$ outside $\odot(O, 8)$. $\overline{OP}$ intersects the circle at $N$. If $NP = 2$,then $PM = \ldots$