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  2. Fagnano's problem - Wikipedia

    en.wikipedia.org/wiki/Fagnano's_problem

    The orthic triangle, with vertices at the base points of the altitudes of the given triangle, has the smallest perimeter of all triangles inscribed into an acute triangle, hence it is the solution of Fagnano's problem.

  3. Solution of triangles - Wikipedia

    en.wikipedia.org/wiki/Solution_of_triangles

    Solution of triangles (Latin: solutio triangulorum) is the main trigonometric problem of finding the characteristics of a triangle (angles and lengths of sides), when some of these are known. The triangle can be located on a plane or on a sphere. Applications requiring triangle solutions include geodesy, astronomy, construction, and navigation.

  4. Acute and obtuse triangles - Wikipedia

    en.wikipedia.org/wiki/Acute_and_obtuse_triangles

    In an acute triangle, the sum of the circumradius R and the inradius r is less than half the sum of the shortest sides a and b: [4]: p.105, #2690 + < +, while the reverse inequality holds for an obtuse triangle. For an acute triangle with medians m a, m b, and m c and circumradius R, we have [4]: p.26, #954

  5. Law of cosines - Wikipedia

    en.wikipedia.org/wiki/Law_of_cosines

    Fig. 1 – A triangle. The angles α (or A), β (or B), and γ (or C) are respectively opposite the sides a, b, and c.. In trigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths of the sides of a triangle to the cosine of one of its angles.

  6. Base (geometry) - Wikipedia

    en.wikipedia.org/wiki/Base_(geometry)

    The extended base of a triangle (a particular case of an extended side) is the line that contains the base. When the triangle is obtuse and the base is chosen to be one of the sides adjacent to the obtuse angle, then the altitude dropped perpendicularly from the apex to the base intersects the extended base outside of the triangle. The area of ...

  7. NYT ‘Connections’ Hints and Answers Today, Saturday, December 14

    www.aol.com/nyt-connections-hints-answers-today...

    If you've been having trouble with any of the connections or words in Saturday's puzzle, you're not alone and these hints should definitely help you out. Plus, I'll reveal the answers further down

  8. Heron's formula - Wikipedia

    en.wikipedia.org/wiki/Heron's_formula

    There are many ways to prove Heron's formula, for example using trigonometry as below, or the incenter and one excircle of the triangle, [7] or as a special case of De Gua's theorem (for the particular case of acute triangles), [8] or as a special case of Brahmagupta's formula (for the case of a degenerate cyclic quadrilateral).

  9. Cole Hauser Will 'Miss' the 'Unbelievable Cast' of ...

    www.aol.com/lifestyle/cole-hauser-miss...

    "Hopefully, we can continue to get in people's living rooms and entertain them the way we have over the last seven years," he says of the future of the Dutton universe

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