Fundamentals of Surveying (FS) Practice Exam

The angle formed by a tangent and a chord in a circle is defined mathematically as being measured by one-half the intercepted arc. This principle arises from the properties of circles where the angles pertaining to tangents and chords have established relationships to the arcs they intercept.

When a tangent and a chord intersect at a point on the circumference of a circle, the angle formed on the exterior of the tangent line directly correlates with the arc that lies between the points defined by the intersection of the chord and the circle. Specifically, the measure of that angle is half the measure of the arc that is subtended by the chord. This is a critical concept in circle geometry and is useful for solving problems involving angles, chords, and arcs in surveying and other applications involving circular measurements.

The understanding of this property not only aids in correctly determining the angle but also reinforces the foundational relationships that exist in circle geometry, demonstrating the interconnectedness of various tools and measurements within the context of surveying. This property is an essential aspect when tackling more complex geometrical challenges or during various design and construction applications involving circular features.