Why is a circle not a convex set? Why is a circle not a convex set?

My attempt: I was googling it, but I didn't find the correct answer, as I didn't understand the explanation why a circle is not a convex set as defined here:



As shown in diagram 1, points A and B and points C and D lie inside the circle, thus I think the circle must be a convex set, as clearly shown in figure 1.

Why isn't the circle a convex set?
They mean just the edge of the circle, without the interior. That is not a convex set.
Because the chord is not placed on the circle.