Segment AB is the diameter of a circle, M is an arbitrary point of the circle

Segment AB is the diameter of a circle, M is an arbitrary point of the circle, which is identical to points A and B. Prove that the angle AMB is equal to 90 degrees.

Given:
a circle with center O and radius OB,
segment AB – diameter of a circle,
point M lies on the circle.
Prove that the angle of AMB is 90 degrees
Evidence:
Consider a circle. AMВ angle inscribed. We know that the inscribed angle is equal to half of the central angle on which it rests. Hence:
angle AMB = 1/2 angle AOB (angle AOB – expanded, that is, equal to 180 degrees);
angle AMB = 1/2 * 180;
angle AMB = (1 * 180) / 2;
angle AMB = (1 * 90) / 1;
angle AMB = 90 degrees.
Proven.