How is the angle formed by two tangents related to arcs?

The angle formed by two tangents intersecting at a point outside of the circle is indeed related to the intercepted arcs of the circle. This angle is calculated using the difference between the measures of the major arc and the minor arc that are cut off by the points of tangency. Specifically, the angle formed by two tangents is equal to half the difference of these two arcs.

To elaborate, if you have a circle and two tangents that meet at a point outside the circle, you can identify and measure the arcs that these tangents touch. The angle formed by the two tangents at the external point is half the difference between the measure of the larger arc (the major arc) and the measure of the smaller arc (the minor arc). This relationship is derived from the properties of angles and arcs in circles, particularly regarding how tangents and secants intersect with circles.

This understanding is crucial in solving problems involving circles, tangents, and angles, as it establishes a clear relationship between linear dimensions (the tangents) and angular measurements (the angles formed by those tangents).