Final answer:
m∠XOY = One-half(a – b). The equation that is correct regarding the diagram of circle O is m∠XOY = One-half(a - b). Tangents XZ and YZ intersect at point Z outside of the circle, forming equal angles. The lengths of arcs a and b are also equal, allowing us to use the equation to find the measure of ∠XOY.
Step-by-step explanation:
The equation that is correct regarding the diagram of circle O is m∠XOY = One-half(a - b).
Tangents XZ and YZ intersect at point Z outside of the circle. The angles formed at Z, denoted as ∠XZY, ∠XOY, ∠YOZ, and ∠XOZ, are equal in measure. Since both arcs a and b are subtended by the same angle, ∠XZY, they are also equal in measure. Therefore, we can say that the length of arc a is equal to the length of arc b.
Since the lengths of arcs a and b are equal, we can use the equation m∠XOY = One-half(a - b) to find the measure of ∠XOY. This equation represents the fact that the measure of ∠XOY is half the difference between the lengths of arcs a and b.