Final answer:
To find the length of the minor arc AB, use the formula for the length of an arc in a circle. Plug in the given values and calculate the length of the arc.
Step-by-step explanation:
To find the length of the minor arc AB, we need to use the given information that m∠AOB=120° and OG=12π. Since GA and GB are tangents, we can use the fact that tangents from a point to a circle are equal in length. This means that GA = GB. We can use the formula for the length of an arc in a circle, which is given by the formula:
Length of arc = (central angle/360°) * 2π * radius
In this case, the central angle is 120° and the radius is 12π. Plugging in these values, we get:
Length of arc AB = (120°/360°) * 2π * 12π = (1/3) * 2π * 12π = 8π²