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  2. Incircle and excircles - Wikipedia

    en.wikipedia.org/wiki/Incircle_and_excircles

    The inradius of the incircle in ... An excircle or escribed circle [2] of the triangle is a circle lying outside the triangle, tangent to one of its sides, ...

  3. Tangential quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Tangential_quadrilateral

    This circle is called the incircle of the quadrilateral or its inscribed circle, its center is the incenter and its radius is called the inradius. Since these quadrilaterals can be drawn surrounding or circumscribing their incircles, they have also been called circumscribable quadrilaterals , circumscribing quadrilaterals , and circumscriptible ...

  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. Law of cotangents - Wikipedia

    en.wikipedia.org/wiki/Law_of_cotangents

    In trigonometry, the law of cotangents is a relationship among the lengths of the sides of a triangle and the cotangents of the halves of the three angles. [1] [2]Just as three quantities whose equality is expressed by the law of sines are equal to the diameter of the circumscribed circle of the triangle (or to its reciprocal, depending on how the law is expressed), so also the law of ...

  6. Heronian triangle - Wikipedia

    en.wikipedia.org/wiki/Heronian_triangle

    Every Heronian triangle has a rational inradius (radius of its inscribed circle): For a general triangle the inradius is the ratio of the area to half the perimeter, and both of these are rational in a Heronian triangle.

  7. Inscribed figure - Wikipedia

    en.wikipedia.org/wiki/Inscribed_figure

    The inradius or filling radius of a given outer figure is the radius of the inscribed circle or sphere, if it exists. The definition given above assumes that the objects concerned are embedded in two- or three- dimensional Euclidean space , but can easily be generalized to higher dimensions and other metric spaces .

  8. Circumcircle - Wikipedia

    en.wikipedia.org/wiki/Circumcircle

    where r is the incircle radius and R is the circumcircle radius; hence the circumradius is at least twice the inradius (Euler's triangle inequality), with equality only in the equilateral case. [ 7 ] [ 8 ]

  9. Tangential polygon - Wikipedia

    en.wikipedia.org/wiki/Tangential_polygon

    This is a circle that is tangent to each of the polygon's sides. ... If the n sides of a tangential polygon are a 1, ..., a n, the inradius (radius of the incircle ...