If two circles touch each other externally,then $\ldots \ldots \ldots \ldots$ common tangents can be drawn to them.

$\odot(P, 3)$ and $\odot(P, 5)$ are two concentric circles. Chord $\overline{AB}$ of $\odot(P, 5)$ touches $\odot(P, 3)$ at $M$. Find $AB$.

$A$ tangent to a circle forms an angle of measure $\ldots \ldots \ldots \ldots$ with the radius drawn at the point of contact. (in $^{\circ}$)

If $P$ is a point in the exterior of the circle,then maximum $\ldots \ldots \ldots \ldots$ tangents can be drawn to a circle from $P.$

Write 'True' or 'False' and give reasons for your answer.
The tangent to the circumcircle of an isosceles triangle $ABC$ at $A$,in which $AB = AC$,is parallel to $BC$.

If $AB$ is a chord of a circle with centre $O$,$AOC$ is a diameter and $AT$ is the tangent at $A$ as shown in the figure. Prove that $\angle BAT = \angle ACB$.