28. Exemplar exercise problems III

1. At one end $A$ of a diameter $AB$ of a circle of radius $5 \ cm$, tangent $XAY$ is drawn to the circle. The length of the chord $CD$ parallel to $XY$ and at a distance $8 \ cm$ from $A$ is

 

2. In figure, $AT$ is a tangent to the circle with centre $O$ such that $OT = 4 \ cm$ and $\angle OTA = 30^\circ$. Then $AT$ is equal to