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2. 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.

3. Intersecting chords theorem - Wikipedia

   en.wikipedia.org/wiki/Intersecting_chords_theorem

   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 by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal. It is Proposition 35 of Book 3 of Euclid's Elements.

4. Inscribed angle - Wikipedia

   en.wikipedia.org/wiki/Inscribed_angle

   As a consequence of the theorem, opposite angles of cyclic quadrilaterals sum to 180°; conversely, any quadrilateral for which this is true can be inscribed in a circle. As another example, the inscribed angle theorem is the basis for several theorems related to the power of a point with respect to a circle. Further, it allows one to prove ...

5. 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 ...

6. Category:Theorems about circles - Wikipedia

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

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7. Gershgorin circle theorem - Wikipedia

   en.wikipedia.org/wiki/Gershgorin_circle_theorem

   Whichever continuity is used in a proof of the Gerschgorin disk theorem, it should be justified that the sum of algebraic multiplicities of eigenvalues remains unchanged on each connected region. A proof using the argument principle of complex analysis requires no eigenvalue continuity of any kind. [1] For a brief discussion and clarification ...