Case14. Elements of an equilateral triangle are numbered as follows:
1 - side \(a\),
2 - radius \(R_1\) of inscribed circle \((R_1 = a \cdot \sqrt{3}/6)\),
3 - radius \(R_2\) of the circumscribed circle \((R_2 = 2 \cdot R_1)\),
4 - area \(S = a^2 \cdot \sqrt{3}/4\).

The number of one of these elements and its value are given. Output the values of the remaining elements of this triangle (in the same order).

import random
import math

r = {1 : "side a", 2 : "radius R1 inscribed circle", \
     3 : "radius R2 circumscribed circle", 4 : "area S"}
d = []

i = random.randrange(1,5)
i = 4
print("i : ", i)
N = random.randrange(1,100)
#N = 64
print(r[i],":",N)
if i == 1:
    a = N
    R1 = a * math.sqrt(3) / 6
    R2 = R1 * 2
    S = a**2 * math.sqrt(3) / 4
elif i == 2:
    R1 = N
    a = R1 * 6 / math.sqrt(3)
    R2 = R1 * 2
    S = a**2 * math.sqrt(3) / 4
elif i == 3:
    R2 = N
    R1 = R2 / 2
    a = R1 * 6 / math.sqrt(3)
    S = a**2 * math.sqrt(3) / 4
elif i == 4:
    S = N
    a = math.sqrt(S * 4 / math.sqrt(3))
    R1 = a * math.sqrt(3) / 6
    R2 = R1 * 2

d.append(a)
d.append(R1)
d.append(R2)
d.append(S)

print()
print("Elements of an equilateral triangle:")
for i in range(0,4):
    print(r[i+1],":",d[i])