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  2. Newton's theorem (quadrilateral) - Wikipedia

    en.wikipedia.org/wiki/Newton's_theorem...

    Newton's theorem can easily be derived from Anne's theorem considering that in tangential quadrilaterals the combined lengths of opposite sides are equal (Pitot theorem: a + c = b + d). According to Anne's theorem, showing that the combined areas of opposite triangles PAD and PBC and the combined areas of triangles PAB and PCD are equal is ...

  3. Ptolemy's theorem - Wikipedia

    en.wikipedia.org/wiki/Ptolemy's_theorem

    Ptolemy's theorem is a relation among these lengths in a cyclic quadrilateral. = + In Euclidean geometry, Ptolemy's theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral (a quadrilateral whose vertices lie on a common circle).

  4. Pitot theorem - Wikipedia

    en.wikipedia.org/wiki/Pitot_theorem

    Pitot's theorem states that, for these quadrilaterals, the two sums of lengths of opposite sides are the same. Both sums of lengths equal the semiperimeter of the quadrilateral. [2] The converse implication is also true: whenever a convex quadrilateral has pairs of opposite sides with the same sums of lengths, it has an inscribed circle ...

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  6. Newton–Gauss line - Wikipedia

    en.wikipedia.org/wiki/Newton–Gauss_line

    The two complete quadrilaterals have a shared diagonal, EF. N lies on the Newton–Gauss line of both quadrilaterals. N is equidistant from G and H, since it is the circumcenter of the cyclic quadrilateral EGFH. If triangles GMP, HMQ are congruent, and it will follow that M lies on the perpendicular bisector of the line HG.

  7. Euler's quadrilateral theorem - Wikipedia

    en.wikipedia.org/wiki/Euler's_quadrilateral_theorem

    Euler's quadrilateral theorem or Euler's law on quadrilaterals, named after Leonhard Euler (1707–1783), describes a relation between the sides of a convex quadrilateral and its diagonals. It is a generalisation of the parallelogram law which in turn can be seen as generalisation of the Pythagorean theorem .

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