Points A and B are marked on the circle centered at point O so that the angle AOB = 110 °. The length of the larger of the arcs into which the circle is divided by points A and B is 125. Find the length of the smaller arc.
The angle corresponding to the larger arc is 360-110 = 250 degrees. Knowing the formula for the length of a circular arc L = πrα / 180, we can find the radius of the circle: r = L * 180 / π * α = 125 * 180 / π * 250 = 180 / π * 2 = 90 / π. Knowing that the AOB angle is 110 degrees, the radius is 90 / π, we can find the length of the smaller arc: l = πrα / 180 = π * (90 / π) * 110/180 = 55.
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