AC-tangent, and AB-chord of the circle centered at point O, angle BAC = 75. What is the angle AOB?

The angle OAC is 90, since the radius OA of the circle is drawn to the point of tangency of the tangent CA with the circle.

Then the angle OAB = 90 – BAC = 90 – 75 = 15.

In the AOC triangle, the sides OA and OB are equal as the radii of a circle, then the AOB triangle is isosceles, which means the angle OAB = OBA = 15.

The sum of the inner angles of the triangle is 180, then the angle AOB = 180 – 15 – 15 = 150.

Answer: The value of the angle AOB is equal to 150.