Through the ends A and B of the circular arc with center O, tangents AC and BC are drawn.

Through the ends A and B of the circular arc with center O, tangents AC and BC are drawn. The CAB angle is 33 °. find the angle AOB.

By the property of tangents drawn from one point, the lengths of such tangents are equal, CA = CB, then the triangle ABC is isosceles, and the angle CBA = CAB = 33.

Then the angle ACB = (180 – 33 – 33) = 114.

The radii ОА and ОВ are perpendicular to the tangents АС and ВС, then, in the quadrangle ОАСВ, ygo AOB = (360 – 90 – 90 – 114) = 66.

Answer: The AOB angle is 66.