In a circle, if A is the center and points B and C are on the circumference of the circle, then the following inequality can be established based on the geometry of circles:
AB + AC > BC.
This is a result of the triangle inequality, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Here, AB and AC are the lengths of two sides of triangle ABC, and BC is the length of the third side.
Therefore, the correct inequality to fill in the blank is:
AB + AC > BC.