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  2. Power of a point - Wikipedia

    en.wikipedia.org/wiki/Power_of_a_point

    Steiner used the power of a point for proofs of several statements on circles, for example: Determination of a circle, that intersects four circles by the same angle. [2] Solving the Problem of Apollonius; Construction of the Malfatti circles: [3] For a given triangle determine three circles, which touch each other and two sides of the triangle ...

  3. Conway circle theorem - Wikipedia

    en.wikipedia.org/wiki/Conway_circle_theorem

    Conway's circle theorem as a special case of the generalisation, called "side divider theorem" (Villiers) or "windscreen wiper theorem" (Polster)) Conway's circle is a special case of a more general circle for a triangle that can be obtained as follows: Given any ABC with an arbitrary point P on line AB.

  4. Six circles theorem - Wikipedia

    en.wikipedia.org/wiki/Six_circles_theorem

    Some examples of theorem configuration changing the radius of the first circle. In the last configuration the circles are pairwise coincident. In geometry, the six circles theorem relates to a chain of six circles together with a triangle, such that each circle is tangent to two sides of the triangle and also to the preceding circle in the ...

  5. 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 ...

  6. Category:Theorems about circles - Wikipedia

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

    Pages in category "Theorems about circles" The following 21 pages are in this category, out of 21 total. This list may not reflect recent changes. B. Butterfly ...

  7. Casey's theorem - Wikipedia

    en.wikipedia.org/wiki/Casey's_theorem

    The following proof is attributable [2] to Zacharias. [3] Denote the radius of circle by and its tangency point with the circle by . We will use the notation , for the centers of the circles. Note that from Pythagorean theorem,

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