For a semicircle, a triangle is drawn whoose bottom side coincides with the diameter of the semicircle. The upper vertex can be moved on the semicircle by dragging the mouse. What do you notice about the angle marked in green?

By the connecting line between the center of the semicircle and the upper vertex, the given triangle is divided into partial triangles. In each of these two partial triangles, two sides are circle radii, i.e. of equal length. The two angles marked in red therefore have the same size, since they are base angles in an isosceles triangle. Similarly, the two angles marked in blue have the same size. If you add the sizes of the angles marked in red or blue, you get 180° (sum of the triangle's interior angles). As a result, the size of the angle drawn in green (one red and one blue angle) must be half, that is equal to 90°.

A triangle inscribed in a semicircle is right.