What defines an inscribed angle in geometry?

An inscribed angle is defined as an angle formed by two chords in a circle that share a common endpoint on the circumference of the circle. This common endpoint is known as the vertex of the angle, while the other two endpoints are points where the chords intersect the circle.

The key characteristic of an inscribed angle is that it intercepts or subtends an arc on the circle, meaning the angle is defined by the two points on the circle that lie on the endpoints of the chords. The measure of the inscribed angle is half the measure of the arc that it intercepts, which is a crucial property that helps in solving many problems related to circle geometry.

In considering the other options, an angle formed by two tangents intersecting outside a circle refers to a different concept in circle geometry, known as an exterior angle, which is not applicable here. Similarly, there is no requirement for an inscribed angle to be larger than a right angle, as it can have various measures, including acute and obtuse angles. Lastly, an angle that is directly at the center of a circle describes a central angle, which differs from the positioning and definition of an inscribed angle. Therefore, the clear and accurate definition of an inscribed angle aligns perfectly