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...

intersecting secants theorem and chord theorem the power of a point plays the role of an invariant: Intersecting secants theorem: For a point P {\displaystyle...

mean value theorem says that given any chord of a smooth curve, we can find a point on the curve lying between the end-points of the chord such that the...

the circle at A and if AQ is a chord of the circle, then ∠DAQ = ⁠1/2⁠arc(AQ). The chord theorem states that if two chords, CD and EB, intersect at A, then...

Constant chord theorem (geometry) Constant rank theorem ( multivariate calculus) Continuous mapping theorem (probability theory) Convolution theorem (Fourier...

Pythagorean theorem. Mamikon's method, however, envisions an alternate construction of the ring: first the inner circle alone is drawn, then a constant-length...

angles, respectively. Theorems on the lengths of chords are applications of the law of sines. And Archimedes' theorem on broken chords is equivalent to formulas...

inequality and Barbier's theorem, the circle has the maximum area of any curve of given constant width. The Blaschke–Lebesgue theorem says that the Reuleaux...

{CM} }}=2r}  (PMCK is a parallelogram). Using the intersecting chords theorem on the chords BC and DE, we get B M ¯ ⋅ C M ¯ = D M ¯ ⋅ E M ¯ . {\displaystyle...

circle's center bisecting a chord is perpendicular to the chord. If the intersection of any two perpendicular chords divides one chord into lengths a and b and...

In mathematics, the Dottie number is a constant that is the unique real root of the equation cos ⁡ x = x {\displaystyle \cos x=x} , where the argument...

a chord. More formally, a circular segment is a plane region bounded by a circular arc (of less than π radians by convention) and the circular chord connecting...

whose endpoints lie on the circle. It can also be defined as the longest chord of the circle. Both definitions are also valid for the diameter of a sphere...

Algebraic curve Arc Asymptote Asymptotic curve Barbier's theorem Bézier curve Bézout's theorem Birch and Swinnerton-Dyer conjecture Bitangent Bitangents...

a uniform fluid at a constant speed so large that the flow seen in the body-fixed frame is steady and unseparated. The theorem relates the lift generated...

}{8}}}-S(1)<\infty ,} where S(x) is the Fresnel integral. Via the convergence theorem along chords, the Borel integral converges for all z ≤ 2 (the integral diverges...

circle's interior. Tangent lines to circles form the subject of several theorems, and play an important role in many geometrical constructions and proofs...

maximal planar graphs to a theorem of Hassler Whitney. Seymour, P. D.; Weaver, R. W. (1984), "A generalization of chordal graphs", Journal of Graph Theory...

Beevers–Lipson strip Constant-Q transform Discrete Fourier transform DFT matrix Fast Fourier transform Fourier integral operator Fourier inversion theorem Fourier...

\dots ,4} , Descartes' theorem says: If one of the four curvatures is considered to be a variable, and the rest to be constants, this is a quadratic equation...

{\delta }} lie on the same circle and subtend the same chord c; thus, by the inscribed angle theorem, γ = δ {\displaystyle {\gamma }={\delta }} . Therefore...

such as in feet. The relationship of versine, chord and radius is derived from the Pythagorean theorem. Based on the diagram on the right: O C = O A 2...

while still an undergraduate, in which he introduced the Lévy–Steinitz theorem. His teacher and advisor was Jacques Hadamard. After graduation, he spent...

points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special type of ellipse in which...

proven to be impossible, as a consequence of the Lindemann–Weierstrass theorem, which proves that pi ( π {\displaystyle \pi } ) is a transcendental number...

the class if a tree-decomposition with constant bounded treewidth is provided. Specifically, Courcelle's theorem states that if a graph problem can be...

editor E (programming language), an object-oriented programming language E (theorem prover), a modern, high performance prover for first-order logic e (verification...

{\displaystyle \cos(\gamma )=0} , the resulting equation becomes the Pythagorean theorem. The cross product and dot product are operations on two vectors in Euclidean...

strong perfect graph theorem as being the graphs with no odd holes or odd anti-holes. The hole-free graphs are the same as the chordal graphs. homomorphic...

concyclic, with different circles; see Nine-point circle and Lester's theorem. The radius of the circle on which lie a set of points is, by definition...