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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 constant chord theorem is a statement in elementary geometry about a property of certain chords in two intersecting circles. The circles k 1 {\displaystyle k_{1}} and k 2 {\displaystyle k_{2}} intersect in the points P {\displaystyle P} and Q {\displaystyle Q} .
There is a Catalan number of chord diagrams on a given ordered set in which no two chords cross each other. [2] The crossing pattern of chords in a chord diagram may be described by a circle graph, the intersection graph of the chords: it has a vertex for each chord and an edge for each two chords that cross. [3]
The chord theorem states that if two chords, CD and EB, intersect at A, then AC × AD = AB × AE. If two secants, AE and AD, also cut the circle at B and C respectively, then AC × AD = AB × AE (corollary of the chord theorem). A tangent can be considered a limiting case of a secant whose ends are coincident.
From a collection of subtrees of a tree, one can define a subtree graph, which is an intersection graph that has one vertex per subtree and an edge connecting any two subtrees that overlap in one or more nodes of the tree. Gavril showed that the subtree graphs are exactly the chordal graphs.
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Maybe we all watched a little too much This Is Us and are still mourning the loss of Jack Pearson, or maybe a kitchen mishap as a child has left us wary of slow cookers. Whatever the case may be ...
In geometry, an inscribed angle is the angle formed in the interior of a circle when two chords intersect on the circle. It can also be defined as the angle subtended at a point on the circle by two given points on the circle. Equivalently, an inscribed angle is defined by two chords of the circle sharing an endpoint.