( 50 POINTS )In order to host track and field competitions, a 400-meter track needs to be created. A typical Olympic track looks like the one on the picture.

a) Show that the runner who runs in the inside lane runs 400 meters.
b) All other runners in a 400 meters race start a little further ahead since their lane is a little longer. If the radius of lane 2 (the one beside the inside lane) is 37.92 meters, find how much of a stagger (head start) the lane 2 runner should be given. Round your answer to the nearest hundredth.