For two secants or tangents from an external point to a circle, the exterior angle equals half the difference of the intercepted arcs. Which statement is true?

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Think about the two arcs on the circle that are cut off by the two lines from the external point. The exterior angle is equal to one-half of the difference between the measures of those two arcs—the larger arc minus the smaller arc. This mirrors how angles relate to intercepted arcs in circle geometry: the one-half factor comes from how inscribed/central-angle measures connect to arc measures. For two tangents, those intercepted arcs are the two arcs between the tangent points, whose difference is the major arc minus the minor arc; halving gives the exterior angle. That’s why this statement is the correct description. If you try the other ideas (sum, average, or a plain difference), you won’t land on the actual exterior angle value.