import turtle
import math

turtle.pensize(2)
turtle.speed("fastest")
radius = 80
count = 50
angle = 360/count

edge = radius/10

print(angle)
print(2*math.cos(math.radians((180-angle)/2)))
R = edge/(2*math.cos(math.radians((180-angle)/2)))

print(R)
turtle.penup()
turtle.goto(0,  (R))
turtle.pendown()

color = ("red", "green","orange", "purple","blue","pink","black","gray")

for _ in range(count):
    turtle.pencolor(color[_ % len(color)])
    turtle.circle(radius)
    turtle.penup()
    turtle.left(angle/2)
    turtle.backward(edge)
    turtle.left(angle/2)
    turtle.pendown()


turtle.done()