ইন্টুইশান: বৃত্ত সর্বদা উত্তল

Definition: A geometric object is convex if, for any two points $A$ and $B$ in the object, the segment $AB$ lies entirely in the interior of the object.

Correct! If you join any two points inside a square, the resulting segment will still be in the square.

Nice! Using the definition, we can see that if you connect any two points in a circle, the resulting segment should be in the circle.

As a bonus, here's another way to think about convexity intuitively. A fun exercise would be to convince yourself why this intuition is true.

Intuition: An object in 2D space is convex if it is "always curving inwards".