At which point does a sphere's edges look flat?

Question

Good Morning, I'm pretty new to the mathematics section of StackExchange so please do forgive me if I make some mistakes in the question.
I'm trying to make a spherical worlds game, however there is one thing I need to consider which is the size of the camera in relation with the world.
What I mean by this is how much of the horizon(when compared to the circumference) should the camera minimally be able to see such that the horizon is almost completely flat, like in the earth or the moon.
Example: take a circle consider its entire circumference(which I will be calling c), it doesn't look flat right? Now do the same but repeatedly decrease the amount of c you actually see. By the time you see a very small part of c it almost looks flat. What is the minimum ratio of the part compared to the whole should it be to be called almost flat?