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  2. Inscribed angle - Wikipedia

    en.wikipedia.org/wiki/Inscribed_angle

    In geometry, an 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 on the circle by two given points on the circle. Equivalently, an inscribed angle is defined by two chords of the circle sharing an endpoint.

  3. Brahmagupta theorem - Wikipedia

    en.wikipedia.org/wiki/Brahmagupta_theorem

    More specifically, let A, B, C and D be four points on a circle such that the lines AC and BD are perpendicular. Denote the intersection of AC and BD by M. Drop the perpendicular from M to the line BC, calling the intersection E. Let F be the intersection of the line EM and the edge AD. Then, the theorem states that F is the midpoint AD.

  4. Category:Theorems about circles - Wikipedia

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

    Download as PDF; Printable version; In other projects ... Pages in category "Theorems about circles" ... Inscribed angle theorem;

  5. Circle - Wikipedia

    en.wikipedia.org/wiki/Circle

    An inscribed angle (examples are the blue and green angles in the figure) is exactly half the corresponding central angle (red). Hence, all inscribed angles that subtend the same arc (pink) are equal. Angles inscribed on the arc (brown) are supplementary. In particular, every inscribed angle that subtends a diameter is a right angle (since the ...

  6. Incircle and excircles - Wikipedia

    en.wikipedia.org/wiki/Incircle_and_excircles

    The nine-point circle is tangent to the incircle and excircles. In geometry, the nine-point circle is a circle that can be constructed for any given triangle. It is so named because it passes through nine significant concyclic points defined from the triangle. These nine points are: [28] [29] The midpoint of each side of the triangle; The foot ...

  7. 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.

  8. Ptolemy's table of chords - Wikipedia

    en.wikipedia.org/wiki/Ptolemy's_table_of_chords

    For tiny arcs, the chord is to the arc angle in degrees as π is to 3, or more precisely, the ratio can be made as close as desired to ⁠ π / 3 ⁠ ≈ 1.047 197 55 by making θ small enough. Thus, for the arc of ⁠ 1 / 2 ⁠ °, the chord length is slightly more than the arc angle in degrees. As the arc increases, the ratio of the chord to ...

  9. 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.

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