How big does the black hole appear to be?
In order to see that, we retrace the paths of photons. If following the path backwards leads into the event horizon (black line), then no photons arrive on this path and the observer's sky is black in this direction. If the photon path passes by the black hole (blue line), photons from distant objects may reach the observer. The border between the sky and the black hole is given by the photon path that turns into the circular orbit (red line).