Chords, Secants, Tangents Oh My!

A tangent is a line that touches a circle at exactly one point, known as the point of tangency.

A secant line is a line that intersects a circle at two points.

A chord is a line segment whose endpoints lie on the circle.

The point of tangency is the point where a tangent line touches the circle.

A tangent can be identified as a line that touches the circle at only one point without crossing it.

All chords are secants, but not all secants are chords. A secant intersects the circle at two points, while a chord is a segment between two points on the circle.

The length of a chord can be calculated using the formula: $$L = 2r \times \text{sin}(\frac{\theta}{2})$$ , where $$L$$ is the length of the chord, $$r$$ is the radius, and $$\theta$$ is the angle in radians.

The secant-tangent theorem states that if a tangent and a secant intersect at a point outside the circle, the square of the length of the tangent segment is equal to the product of the lengths of the entire secant segment and its external segment.

The angle formed by two tangents from a point outside the circle is equal to half the difference of the measures of the intercepted arcs.

The angle formed by two intersecting chords is equal to the average of the measures of the arcs intercepted by the angle and its vertical angle.