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\includegraphics[max width=\textwidth, alt={}, center]{02da6b6a-6db1-4bc3-ad4e-537e4f61dcac-3_365_663_1813_740} The inside lane of a school running track consists of two straight sections each of length \(x\) metres, and two semicircular sections each of radius \(r\) metres, as shown in the diagram. The straight sections are perpendicular to the diameters of the semicircular sections. The perimeter of the inside lane is 400 metres.

1. Show that the area, \(A \mathrm {~m} ^ { 2 }\), of the region enclosed by the inside lane is given by \(A = 400 r - \pi r ^ { 2 }\).
2. Given that \(x\) and \(r\) can vary, show that, when \(A\) has a stationary value, there are no straight sections in the track. Determine whether the stationary value is a maximum or a minimum. [5]