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  2. Circumcircle - Wikipedia

    en.wikipedia.org/wiki/Circumcircle

    The circumcenter's position depends on the type of triangle: For an acute triangle (all angles smaller than a right angle), the circumcenter always lies inside the triangle. For a right triangle, the circumcenter always lies at the midpoint of the hypotenuse. This is one form of Thales' theorem.

  3. Euler's theorem in geometry - Wikipedia

    en.wikipedia.org/wiki/Euler's_theorem_in_geometry

    In geometry, Euler's theorem states that the distance d between the circumcenter and incenter of a triangle is given by [1] [2] = or equivalently + + =, where and denote the circumradius and inradius respectively (the radii of the circumscribed circle and inscribed circle respectively).

  4. Triangle center - Wikipedia

    en.wikipedia.org/wiki/Triangle_center

    In geometry, a triangle center or triangle centre is a point in the triangle's plane that is in some sense in the middle of the triangle. For example, the centroid, circumcenter, incenter and orthocenter were familiar to the ancient Greeks, and can be obtained by simple constructions.

  5. Cyclic quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Cyclic_quadrilateral

    In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle. This circle is called the circumcircle or circumscribed circle, and the vertices are said to be concyclic. The center of the circle and its radius are called the circumcenter and the circumradius respectively.

  6. Euler line - Wikipedia

    en.wikipedia.org/wiki/Euler_line

    In geometry, the Euler line, named after Leonhard Euler (/ ˈ ɔɪ l ər / OY-lər), is a line determined from any triangle that is not equilateral.It is a central line of the triangle, and it passes through several important points determined from the triangle, including the orthocenter, the circumcenter, the centroid, the Exeter point and the center of the nine-point circle of the triangle.

  7. Nine-point circle - Wikipedia

    en.wikipedia.org/wiki/Nine-point_circle

    The conic is an ellipse when P is interior to ABC or in a region sharing vertical angles with the triangle, but a nine-point hyperbola occurs when P is in one of the three adjacent regions, and the hyperbola is rectangular when P lies on the circumcircle of ABC.

  8. 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.

  9. Circumconic and inconic - Wikipedia

    en.wikipedia.org/wiki/Circumconic_and_inconic

    In Euclidean geometry, a circumconic is a conic section that passes through the three vertices of a triangle, [1] and an inconic is a conic section inscribed in the sides, possibly extended, of a triangle. [2] Suppose A, B, C are distinct non-collinear points, and let ABC denote the triangle whose vertices are A, B, C.

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