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  2. Circumcircle - Wikipedia

    en.wikipedia.org/wiki/Circumcircle

    In geometry, the circumscribed circle or circumcircle of a triangle is a circle that passes through all three vertices. The center of this circle is called the circumcenter of the triangle, and its radius is called the circumradius .

  3. Circumscribed circle - Wikipedia

    en.wikipedia.org/wiki/Circumscribed_circle

    In geometry, a circumscribed circle for a set of points is a circle passing through each of them. Such a circle is said to circumscribe the points or a polygon formed from them; such a polygon is said to be inscribed in the circle. Circumcircle, the circumscribed circle of a triangle, which always exists for a given triangle.

  4. 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).

  5. Triangle center - Wikipedia

    en.wikipedia.org/wiki/Triangle_center

    Center of the triangle's inscribed circle. X 2: Centroid: G:: Intersection of the medians. Center of mass of a uniform triangular lamina. X 3: Circumcenter: O ⁡: ⁡: ⁡ Intersection of the perpendicular bisectors of the sides. Center of the triangle's circumscribed circle. X 4: Orthocenter: H

  6. Triangle - Wikipedia

    en.wikipedia.org/wiki/Triangle

    The tangential triangle of a reference triangle (other than a right triangle) is the triangle whose sides are on the tangent lines to the reference triangle's circumcircle at its vertices. [ 64 ] As mentioned above, every triangle has a unique circumcircle, a circle passing through all three vertices, whose center is the intersection of the ...

  7. Incircle and excircles - Wikipedia

    en.wikipedia.org/wiki/Incircle_and_excircles

    An excircle or escribed circle [2] of the triangle is a circle lying outside the triangle, tangent to one of its sides and tangent to the extensions of the other two. Every triangle has three distinct excircles, each tangent to one of the triangle's sides.

  8. Concyclic points - Wikipedia

    en.wikipedia.org/wiki/Concyclic_points

    A sequence of circumscribed polygons and circles. Any regular polygon is cyclic. Consider a unit circle, then circumscribe a regular triangle such that each side touches the circle. Circumscribe a circle, then circumscribe a square. Again circumscribe a circle, then circumscribe a regular pentagon, and so on.

  9. Inscribed figure - Wikipedia

    en.wikipedia.org/wiki/Inscribed_figure

    Every circle has an inscribed triangle with any three given angle measures (summing of course to 180°), and every triangle can be inscribed in some circle (which is called its circumscribed circle or circumcircle). Every triangle has an inscribed circle, called the incircle.