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  2. Nine-point circle - Wikipedia

    en.wikipedia.org/wiki/Nine-point_circle

    The nine-point circles are all congruent with a radius of half that of the cyclic quadrilateral's circumcircle. The nine-point circles form a set of four Johnson circles. Consequently, the four nine-point centers are cyclic and lie on a circle congruent to the four nine-point circles that is centered at the anticenter of the cyclic quadrilateral.

  3. Category:Theorems about circles - Wikipedia

    en.wikipedia.org/.../Category:Theorems_about_circles

    Download as PDF; Printable version; In other projects Wikidata item; ... Pages in category "Theorems about circles" The following 21 pages are in this category, out ...

  4. List of theorems - Wikipedia

    en.wikipedia.org/wiki/List_of_theorems

    Clausius theorem ; Clifford's circle theorems (Euclidean plane geometry) Clifford's theorem on special divisors (algebraic curves) Closed graph theorem (functional analysis) Closed range theorem (functional analysis) Cluster decomposition theorem (quantum field theory) Coase theorem ; Cochran's theorem

  5. Power of a point - Wikipedia

    en.wikipedia.org/wiki/Power_of_a_point

    Due to the Pythagorean theorem the number () has the simple geometric meanings shown in the diagram: For a point outside the circle () is the squared tangential distance | | of point to the circle . Points with equal power, isolines of Π ( P ) {\displaystyle \Pi (P)} , are circles concentric to circle c {\displaystyle c} .

  6. Mathematics - Wikipedia

    en.wikipedia.org/wiki/Mathematics

    Around 300 BC, Euclid organized mathematical knowledge by way of postulates and first principles, which evolved into the axiomatic method that is used in mathematics today, consisting of definition, axiom, theorem, and proof. [78] His book, Elements, is widely considered the most successful and influential textbook of all time. [79]

  7. Thales's theorem - Wikipedia

    en.wikipedia.org/wiki/Thales's_theorem

    In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ∠ ABC is a right angle. Thales's theorem is a special case of the inscribed angle theorem and is mentioned and proved as part of the 31st proposition in the third book of Euclid's Elements. [1]

  8. Circle theorem - Wikipedia

    en.wikipedia.org/wiki/Circle_theorem

    Circle theorem may refer to: Any of many theorems related to the circle; often taught as a group in GCSE mathematics. These include: Inscribed angle theorem. Thales' theorem, if A, B and C are points on a circle where the line AC is a diameter of the circle, then the angle ∠ABC is a right angle. Alternate segment theorem. Ptolemy's theorem.

  9. Nine-point center - Wikipedia

    en.wikipedia.org/wiki/Nine-point_center

    A triangle showing its circumcircle and circumcenter (black), altitudes and orthocenter (red), and nine-point circle and nine-point center (blue) In geometry , the nine-point center is a triangle center , a point defined from a given triangle in a way that does not depend on the placement or scale of the triangle.