O-center of the circle, AC-tangent to the circle, angle BAC = 80 degrees. Find the corner of the BAO.

A straight line tangent to the circle and the radius that abuts against the tangent point form a right angle:
CAO angle = 90 degrees.
The same angle is equal to the sum of the angles: CAO angle = CAB angle + BAO angle (1)
By condition, the angle BAC = 80 degrees
Substituting the values of the angles into equality (1), we obtain
90grad. = 80 deg. + angle BAO
angle BAO = 10 deg.
Answer: 10 degrees.