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  2. Special cases of Apollonius' problem - Wikipedia

    en.wikipedia.org/wiki/Special_cases_of_Apollonius...

    A circle is tangent to a point if it passes through the point, and tangent to a line if they intersect at a single point P or if the line is perpendicular to a radius drawn from the circle's center to P. Circles tangent to two given points must lie on the perpendicular bisector. Circles tangent to two given lines must lie on the angle bisector.

  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. Problem of Apollonius - Wikipedia

    en.wikipedia.org/wiki/Problem_of_Apollonius

    Circles are generally transformed into other circles under inversion; however, if a circle passes through the center of the inversion circle, it is transformed into a straight line, and vice versa. Importantly, if a circle crosses the circle of inversion at right angles (intersects perpendicularly), it is left unchanged by the inversion; it is ...

  5. List of circle topics - Wikipedia

    en.wikipedia.org/wiki/List_of_circle_topics

    Dinostratus' theorem; Dividing a circle into areas – Problem in geometry; Equal incircles theorem – On rays from a point to a line, with equal inscribed circles between adjacent rays; Five circles theorem – Derives a pentagram from five chained circles centered on a common sixth circle; Gauss circle problem – How many integer lattice ...

  6. 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]

  7. Clifford's circle theorems - Wikipedia

    en.wikipedia.org/wiki/Clifford's_circle_theorems

    The second theorem considers five circles in general position passing through a single point M. Each subset of four circles defines a new point P according to the first theorem. Then these five points all lie on a single circle C. The third theorem considers six circles in general position that pass through a single point M. Each subset of five ...

  8. NFL Week 14 betting: 7 best lines, props and more, including ...

    www.aol.com/sports/nfl-week-14-betting-7...

    The only time they won but didn't cover during that streak was Week 9, when they didn't cover as 7.5-point favorites against the Jacksonville Jaguars in a 28-23 win.

  9. Gauss circle problem - Wikipedia

    en.wikipedia.org/wiki/Gauss_circle_problem

    Gauss's circle problem asks how many points there are inside this circle of the form (,) where and are both integers. Since the equation of this circle is given in Cartesian coordinates by x 2 + y 2 = r 2 {\displaystyle x^{2}+y^{2}=r^{2}} , the question is equivalently asking how many pairs of integers m and n there are such that

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