Drawing a great circle

import matplotlib.pyplot as plt
import cartopy.crs as ccrs

ax = plt.axes(projection=ccrs.Robinson())

ax.set_global()

ax.coastlines()

plt.plot([-0.08, 132], [51.53, 43.17], color='red',  transform=ccrs.Geodetic())
plt.plot([-0.08, 132], [51.53, 43.17], color='blue', transform=ccrs.PlateCarree())

plt.show()

(Source code, png)