As shown in the picture, there are five runways on the playground of Guangming primary school, with a total length of 200 meters. Each runway is 0.8 meters wide. The diameter of the semicircle at the innermost bend is 30 meters (1) What are the inner radius of the second and fourth curve respectively? (2) If the 200 meter race, standing in the fifth lane of the small army coin, standing in the second lane of the small strong start about how many meters ahead of time?

As shown in the picture, there are five runways on the playground of Guangming primary school, with a total length of 200 meters. Each runway is 0.8 meters wide. The diameter of the semicircle at the innermost bend is 30 meters (1) What are the inner radius of the second and fourth curve respectively? (2) If the 200 meter race, standing in the fifth lane of the small army coin, standing in the second lane of the small strong start about how many meters ahead of time?

1. The inner radius of the second curve is 15 + 0.8 = 15.8m,
The inner radius of the fourth curve is 15 + 0.8 × 3 = 17.4M
2. The total length of the fifth circle is 200-30 π + 2 × (15 + 0.8 × 4) π = 200 + 6.4 π,
(200-30 π) △ 2 ≈ 52.9 m ＞ 6.4 π M = 20.1 m,
Therefore, in the 200m race, the Xiaojun who stands in the fifth lane starts about 20.1 meters earlier than the Xiaoqiang who stands in the second lane

Six athletes run the 200 meter race, each track is about 1.2 meters wide, and the curve part is semicircle
【1】 If the radius of the innermost curve is 31.7m, what is the total length of the inner curve?
【2】 What is the diameter of the second turn of the inner circle and the total length of the second turn of the inner circle?

【1】 If the radius of the innermost curve is 31.7m, what is the total length of the inner curve?
31.7 × 2 × 3.14 = 199.076 (m)
【2】 What is the diameter of the second turn of the inner circle?
(31.7 + 1.2) × 2 = 65.8 (m)
How many meters is the total length of the second turn inside?
65.8 × 3.14 = 206.612 (m)

The length of straight track in track and field track is the same, so we can find out the difference of adjacent track length by calculating

Well, I suggest you use trigonometric function to solve this problem. As long as you know the angle between curve and straight, the length of two chords is OK