Tangents AC and BC are drawn through the ends A and B of the circular

Tangents AC and BC are drawn through the ends A and B of the circular arc with center O. The smaller arc AB is 64 degrees. find the angle ACB.

From point O, the center of the circle, draw the segments OA and OB to the points of tangency A and B.

By the property of tangents, the radii drawn from the tangent point are perpendicular to the tangents.

The central angle AOB rests on the arc AB, the degree measure of which is 64, then the central angle AOB = 64.

In the quadrangle ОАСВ, the angles ОАС and ОВС are straight, and the sum of internal angles is 3600, then the angle АСВ = (360 – 90 – 90 – 64) = 116.

Answer: Angle ACB = 116.