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Next to the intersecting chords theorem and the tangent-secant theorem, the intersecting secants theorem represents one of the three basic cases of a more general theorem about two intersecting lines and a circle - the power of point theorem.
Menelaus's theorem, case 1: line DEF passes inside triangle ABC. In Euclidean geometry, Menelaus's theorem, named for Menelaus of Alexandria, is a proposition about triangles in plane geometry. Suppose we have a triangle ABC, and a transversal line that crosses BC, AC, AB at points D, E, F respectively, with D, E, F distinct from A, B, C. A ...
In Euclidean geometry, the intersecting chords theorem, or just the chord theorem, is a statement that describes a relation of the four line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal.
The edges or panels of the arrangement are one-dimensional regions belonging to a single line. They are the open line segments and open infinite rays into which each line is partitioned by its crossing points with the other lines. That is, if one of the lines is cut by all the other lines, these are the connected components of its uncut points. [1]
The intercept theorem, also known as Thales's theorem, basic proportionality theorem or side splitter theorem, is an important theorem in elementary geometry about the ratios of various line segments that are created if two rays with a common starting point are intercepted by a pair of parallels.
The Radon point of any four points in the plane is their geometric median, the point that minimizes the sum of distances to the other points. [5] [6] Radon's theorem forms a key step of a standard proof of Helly's theorem on intersections of convex sets; [7] this proof was the motivation for Radon's original discovery of Radon's theorem.
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