Points A and B divide the circle into two arcs, the lengths of which are related as 9:11.

Points A and B divide the circle into two arcs, the lengths of which are related as 9:11. Find the value of the center angle, resting on the smaller of the arcs.

The ratio of the lengths of the circular arcs is 9/11, then the ratio of the degree measures of these arcs will also be equal to 9/11.

Let the degree measure of the smaller arc AB be equal to 9 * X0, then the degree measure of the larger arc AB is equal to 11 * X0.

The degree measure of the circle is 3600, then 9 * X + 11 * X = 360.

X = 360/20 = 18.

Degree measure of the smaller arc AB = 9 * 18 = 162.

The central angle AOB, which is supported by no less arc AB, is equal to its degree measure.

Angle AOB = 162.

Answer: The value of the central angle is 162.