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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 ...
Theorems about quadrilaterals and circles (6 P) Pages in category "Theorems about quadrilaterals" The following 11 pages are in this category, out of 11 total.
Download as PDF; Printable version; In other projects Wikidata item; ... Pages in category "Theorems about quadrilaterals and circles" The following 6 pages are in ...
Download as PDF; Printable version; In other projects ... Theorems about quadrilaterals (1 C, 11 P) ... Pages in category "Quadrilaterals" The following 9 pages are ...
A triangle may be regarded as a quadrilateral with one side of length zero. From this perspective, as d approaches zero, a cyclic quadrilateral converges into a cyclic triangle (all triangles are cyclic), and Brahmagupta's formula simplifies to Heron's formula. If the semiperimeter is not used, Brahmagupta's formula is
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 ...
A quadrilateral is a kite if and only if any one of the following conditions is true: The four sides can be split into two pairs of adjacent equal-length sides. [7] One diagonal crosses the midpoint of the other diagonal at a right angle, forming its perpendicular bisector. [9] (In the concave case, the line through one of the diagonals bisects ...
An arbitrary quadrilateral and its diagonals. Bases of similar triangles are parallel to the blue diagonal. Ditto for the red diagonal. The base pairs form a parallelogram with half the area of the quadrilateral, A q, as the sum of the areas of the four large triangles, A l is 2 A q (each of the two pairs reconstructs the quadrilateral) while that of the small triangles, A s is a quarter of A ...