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...

Point Theorem at cut-the-knot Pythagorean Theorem (Proof #22) at cut-the-knot Intersecting Chords Theorem at cut-the-knot Intersecting Chords Theorem With...

geometry, the intersecting secants theorem or just secant theorem describes the relation of line segments created by two intersecting secants and the...

other chords AB and CD are drawn; AD and BC intersect chord PQ at X and Y correspondingly. Then M is the midpoint of XY. A formal proof of the theorem is...

tangent-secant theorem can be proven using similar triangles (see graphic). Like the intersecting chords theorem and the intersecting secants theorem, the tangent-secant...

triangle. The theorem can also be thought of as a special case of the intersecting chords theorem for a circle, since the converse of Thales' theorem ensures...

of the diameter, with length 2r − H. Applying the intersecting chords theorem to these two chords produces H ( 2 r − H ) = ( W 2 ) 2 , {\displaystyle...

CD}}\end{aligned}}} Casey's theorem Intersecting chords theorem Greek mathematics C. Ptolemy, Almagest, Book 1, Chapter 10. Wilson, Jim. "Ptolemy's Theorem." link verified...

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...

{\mathrm {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...

In geometry, Apollonius's theorem is a theorem relating the length of a median of a triangle to the lengths of its sides. It states that the sum of the...

known as the intersecting chords theorem since the diagonals of the cyclic quadrilateral are chords of the circumcircle. Ptolemy's theorem expresses the...

angle theorem (geometry) Intercept theorem (Euclidean geometry) Intersecting chords theorem (Euclidean geometry) Intersecting secants theorem (Euclidean...

the later tradition of Alexandria. In the Elements, Euclid deduced the theorems from a small set of axioms. He also wrote works on perspective, conic sections...

theorem Intersecting chords theorem Intersecting secants theorem Law of cosines Pons asinorum Pythagorean theorem Tangent-secant theorem Thales's theorem Theorem...

Beltrami-Klein model are two non-intersecting chords. But they actually intersect outside the circle. The polar of the intersecting point is the desired common...

the circular arc on the boundary. Scale of chords Ptolemy's table of chords Holditch's theorem, for a chord rotating in a convex closed curve Circle graph...

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

any two perpendicular chords intersecting at a given point is the same as that of any other two perpendicular chords intersecting at the same point, and...

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...

geometry, the midpoint theorem describes a property of parallel chords in a conic. It states that the midpoints of parallel chords in a conic are located...

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 AC × AD...

lines instead of chords can help to unify statements. As an example of this consider the result: If two secant lines contain chords AB and CD in a circle...

Greek mathematics is obscure, and traditional narratives of mathematical theorems found before the fifth century BC are regarded as later inventions. It...

Every chord that is cut by another (i.e., chords not in group 1) must contain two group 3 edges, its beginning and ending chordal segments. As chords are...

astronomy as modeled by the celestial sphere. Primarily consisting of theorems which were known at least informally a couple centuries earlier, the Spherics...

examination paper. A variant of this theorem states that if one draws line F J {\displaystyle FJ} in such a way that it intersects c P {\displaystyle c_{P}} for...

theorem Intersecting chords theorem Intersecting secants theorem Law of cosines Pons asinorum Pythagorean theorem Tangent-secant theorem Thales's theorem Theorem...

In geometry, Descartes' theorem states that for every four kissing, or mutually tangent circles, the radii of the circles satisfy a certain quadratic...

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...