Question

explore: what do you notice?
ac is the diameter of the circle.
try moving point b around the green semicircle.
what do you notice about the angle $\angle b$?

Explanation:

This is related to the Thales' theorem in geometry. Thales' theorem states that if you have a triangle inscribed in a circle where one side of the triangle is the diameter of the circle, then the angle opposite that side (the angle subtended by the diameter) is a right angle (90 degrees). So as point B moves along the semicircle, angle ∠B should always remain 90 degrees because AC is the diameter, and triangle ABC is inscribed with AC as the diameter.

Answer:

As point B moves around the green semicircle, the angle ∠B remains a right angle (90°) at all times. This is due to Thales' theorem, which states that an angle inscribed in a semicircle is a right angle, since AC is the diameter of the circle.