The diagram shown below is part of a model drawing of the neighbourhood. Block \(B\) is due east of Block \(A\). Block \(C\) has a bearing of \(300^\circ\) from \(B\). The distance between Block \(B\) and Block \(C\) is \(8\text{ cm}\).
Mark and label the position of Block \(C\) on the model drawing.[1]
On the same diagram, construct the perpendicular bisector of the line \(AB\).[1]
A letterbox is to be positioned such that it is equidistant from the three blocks.
On the same diagram, mark \(L\) to represent the position of the letterbox.[2]
Given that the actual distance of \(AB=4\text{ km}\), calculate the actual distance between Block \(C\) and the letterbox, in kilometres.[1]