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  2. 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.

  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. Mixtilinear incircles of a triangle - Wikipedia

    en.wikipedia.org/wiki/Mixtilinear_incircles_of_a...

    In plane geometry, a mixtilinear incircle of a triangle is a circle which is tangent to two of its sides and internally tangent to its circumcircle. The mixtilinear incircle of a triangle tangent to the two sides containing vertex A {\displaystyle A} is called the A {\displaystyle A} -mixtilinear incircle.

  5. Soddy circles of a triangle - Wikipedia

    en.wikipedia.org/wiki/Soddy_circles_of_a_triangle

    When the outer Soddy circle has positive curvature, both Soddy centers are equal detour points. When the outer Soddy circle has negative curvature, its center is the isoperimetric point: the triangles ABP 2, BCP 2, and CAP 2 have equal perimeter. In geometry, the Soddy circles of a triangle are two circles associated with any triangle in the

  6. Semiperimeter - Wikipedia

    en.wikipedia.org/wiki/Semiperimeter

    The area A of any triangle is the product of its inradius (the radius of its inscribed circle) and its semiperimeter: A = r s . {\displaystyle A=rs.} The area of a triangle can also be calculated from its semiperimeter and side lengths a, b, c using Heron's formula :

  7. Circumcircle - Wikipedia

    en.wikipedia.org/wiki/Circumcircle

    Hence, given the radius, r, center, P c, a point on the circle, P 0 and a unit normal of the plane containing the circle, ⁠ ^, ⁠ one parametric equation of the circle starting from the point P 0 and proceeding in a positively oriented (i.e., right-handed) sense about ⁠ ^ ⁠ is the following:

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