The chord AB divides the circular arc with the center O into two parts, the ratio of which is 6: 9. Find the value of the central angle AOB (in degrees), if the arc AB has a smaller degree measure.
Let the degree value of the smaller arc AB = 6 * X0, then the degree measure of the larger arc, by condition, is equal to 9 * X0.
Since the degree measure of a complete circle is 3600, then 6 * X + 9 * X = 360.
15 * X = 360.
X = 360/15 = 24. Then the degree measure of the smaller arc AB = 24 * 6 = 144.
The value of the central angle is equal to the degree measure of the arc on which this angle rests.
Angle AOB = 144.
Answer: Angle AOB = 144.
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