What is a chording theorem?

What is a chording theorem?

• A. A principle regarding tangent lines to circles
• B. A theorem about the area of a triangle
• C. A principle involving the intersection of chords within a circle
• D. A rule defining the properties of parallel lines

Answer: (C)

A chording theorem refers to a principle that involves the relationship and properties concerning the intersection of chords within a circle. When two chords intersect inside a circle, the segments of these chords have a specific multiplicative relationship: the products of the lengths of the segments of each chord are equal. This can be expressed mathematically as if two chords AB and CD intersect at E, then AE * EB = CE * ED. This concept is fundamental in circle geometry and provides insight into how different line segments behave in the context of a circle's properties. Understanding this theorem is essential for solving various geometric problems involving circles.

A chording theorem refers to a principle that involves the relationship and properties concerning the intersection of chords within a circle. When two chords intersect inside a circle, the segments of these chords have a specific multiplicative relationship: the products of the lengths of the segments of each chord are equal. This can be expressed mathematically as if two chords AB and CD intersect at E, then AE * EB = CE * ED. This concept is fundamental in circle geometry and provides insight into how different line segments behave in the context of a circle's properties. Understanding this theorem is essential for solving various geometric problems involving circles.