What is the relationship between the angles formed by two secants that intersect outside a circle?

When two secants intersect outside a circle, the angle formed between the secants has a specific relationship with the arcs that they intercept on the circle. This relationship states that the measure of the angle is equal to half the difference between the measures of the larger arc (the major arc) and the smaller arc (the minor arc) that lie within the circle.

To clarify, if you have two secants that intersect outside the circle, the angle at that intersection can be calculated by taking the measure of the major arc and subtracting the measure of the minor arc, and then dividing that result by 2. This formula is grounded in the properties of angles and arcs in circles and helps in understanding how angles can relate geometrically to the parts of the circle they are associated with.

Thus, the correct answer aligns perfectly with this geometric principle, highlighting the fundamental characteristics of circle theorems involving secants and inscribed angles.