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