Staggered starts on a running track

A running track has two straight sections, each \(100\) m long, joined by two semicircular bends. Measured along the inside edge of lane \(1\), one lap is \(400\) m. Each lane is \(1.2\) m wide. Assume each runner runs along the inside edge of their own lane.

1. Find the radius of the inside edge of lane \(1\) on the bends.[2]
2. Find how much further a runner in lane \(2\) travels than a runner in lane \(1\) in one complete lap.[2]
3. Show that the extra distance for lane \(n\) compared with lane \(1\) is \(2.4\pi(n-1)\) m, and explain why it does not depend on the radius of the bends.[2]
4. In a \(400\) m race, lane \(1\) starts at the finish line. How far ahead must the runner in lane \(8\) start? Give one reason why the real stagger may differ.[2]