If an observer views a dense, dusty torus surrounding a star, what viewing angle results in the appearance of a thin circle?

Answer

Edge-on viewing.

When the observer is looking edge-on to a dense, dusty torus, the geometry causes the structure to project onto the sky as a thin ring or circle.

If an observer views a dense, dusty torus surrounding a star, what viewing angle results in the appearance of a thin circle?
starsexpansionastrophysicssupernova remnantsshock waves