5 The diagram shows the perimeter of a 400 m running track. It consists of a rectangle measuring 100 m by d metres and two semicircles of diameter d metres. The length of each semicircular arc is 100 m. (a) Calculate d. (b) Calculate the total area of the region inside the running track. (c) S is the starting point and finishing point for the 400 m race for a runner in the inside lane. A runner in an outer lane is always 3 m from the inner perimeter. The runner in the outer lane starts at A, runs 400 m and finishes at T. TS = 3 m. (i) Calculate the length of the arc TA. (ii) O is the centre of a semi-circular part of the track. Calculate AOTˆ .