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

Fill in the blanks:
$(i)$ $A$ tangent to a circle intersects it in $.........$ point$(s)$.
$(ii)$ $A$ line intersecting a circle in two points is called a $.........$

$A$ quadrilateral $ABCD$ is drawn to circumscribe a circle (see figure). Prove that $AB + CD = AD + BC$.

If $d_{1}$ and $d_{2}$ $(d_{2} > d_{1})$ are the diameters of two concentric circles and $c$ is the length of a chord of the outer circle which is tangent to the inner circle,prove that $d_{2}^{2} = c^{2} + d_{1}^{2}$.

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.

In $\Delta ABC$,if $AB = 7, BC = 24, AC = 25$,then the diameter of a circle touching all the three sides of the triangle is ............