enow.com Web Search

Search results

  1. Results from the WOW.Com Content Network
  2. Malfatti circles - Wikipedia

    en.wikipedia.org/wiki/Malfatti_circles

    Label the three sides of the given triangle as a, b, and c, and label the three bitangents that are not angle bisectors as x, y, and z, where x is the bitangent to the two circles that do not touch side a, y is the bitangent to the two circles that do not touch side b, and z is the bitangent to the two circles that do not touch side c. Then the ...

  3. Descartes' theorem - Wikipedia

    en.wikipedia.org/wiki/Descartes'_theorem

    Kissing circles. Given three mutually tangent circles (black), there are, in general, two possible answers (red) as to what radius a fourth tangent circle can have.In geometry, Descartes' theorem states that for every four kissing, or mutually tangent circles, the radii of the circles satisfy a certain quadratic equation.

  4. Soddy circles of a triangle - Wikipedia

    en.wikipedia.org/wiki/Soddy_circles_of_a_triangle

    Each of the three circles centered at the vertices crosses two sides of the triangle at right angles, at one of the three intouch points of the triangle, where its incircle is tangent to the side. The two circles tangent to these three circles are separated by the incircle, one interior to it and one exterior.

  5. Trilinear coordinates - Wikipedia

    en.wikipedia.org/wiki/Trilinear_coordinates

    If the parameters l, m, n respectively equal the side lengths a, b, c (or the sines of the angles opposite them) then the equation gives the circumcircle. [1]: p. 199 Each distinct circumconic has a center unique to itself. The equation in trilinear coordinates of the circumconic with center x' : y' : z' is [1]: p. 203

  6. Solution of triangles - Wikipedia

    en.wikipedia.org/wiki/Solution_of_triangles

    A triangle can be uniquely determined in this sense when given any of the following: [1] [2] Three sides (SSS) Two sides and the included angle (SAS, side-angle-side) Two sides and an angle not included between them (SSA), if the side length adjacent to the angle is shorter than the other side length. A side and the two angles adjacent to it (ASA)

  7. Spherical law of cosines - Wikipedia

    en.wikipedia.org/wiki/Spherical_law_of_cosines

    Given a unit sphere, a "spherical triangle" on the surface of the sphere is defined by the great circles connecting three points u, v, and w on the sphere (shown at right). If the lengths of these three sides are a (from u to v ), b (from u to w ), and c (from v to w ), and the angle of the corner opposite c is C , then the (first) spherical ...

  8. Mixtilinear incircles of a triangle - Wikipedia

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

    Then, the image of the -excircle under is a circle internally tangent to sides , and the circumcircle of , that is, the -mixtilinear incircle. Therefore, the A {\displaystyle A} -mixtilinear incircle exists and is unique, and a similar argument can prove the same for the mixtilinear incircles corresponding to B {\displaystyle B} and C ...

  9. Special cases of Apollonius' problem - Wikipedia

    en.wikipedia.org/wiki/Special_cases_of_Apollonius...

    In general, the same inversion transforms the given line L and given circle C into two new circles, c 1 and c 2. Thus, the problem becomes that of finding a solution line tangent to the two inverted circles, which was solved above. There are four such lines, and re-inversion transforms them into the four solution circles of the Apollonius problem.