The scale drawing shows the position of the visitor centre at \(A\) and two straight cycling paths, \(AP\) and \(AQ\) in a park.
A scenic lookout tower is located on a bearing of \(065^\circ\) and is 260 m from \(A\). Mark and label the position of the lookout tower with the letter ‘T’.[1]
A straight footpath, within the park, starting from \(A\) runs exactly halfway between the two cycling paths \(AP\) and \(AQ\). Construct the line representing this footpath till the boundary of the park.[1]
A vending machine is to be placed within the park, such that it is equidistant from \(AP\) and \(AQ\), and equidistant from \(A\) and \(P\). Mark and label the position of the vending machine with the letter ‘X’.[1]