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Quadrilaterals Formed by Perpendicular Bisectors, Projective Collinearity and Interactive Classification of Quadrilaterals from cut-the-knot; Definitions and examples of quadrilaterals and Definition and properties of tetragons from Mathopenref; A (dynamic) Hierarchical Quadrilateral Tree at Dynamic Geometry Sketches
Other names for these quadrilaterals are concyclic quadrilateral and chordal quadrilateral, the latter since the sides of the quadrilateral are chords of the circumcircle. Usually the quadrilateral is assumed to be convex, but there are also crossed cyclic quadrilaterals. The formulas and properties given below are valid in the convex case.
Indian mathematics emerged and developed in the Indian subcontinent [1] from about 1200 BCE [2] until roughly the end of the 18th century CE (approximately 1800 CE). In the classical period of Indian mathematics (400 CE to 1200 CE), important contributions were made by scholars like Aryabhata, Brahmagupta, Bhaskara II, Varāhamihira, and Madhava.
Narayana is also made contributions to algebra and magic squares.Narayana's other major works contain a variety of investigations into the second order indeterminate equation nq 2 + 1 = p 2 (Pell's equation), solutions of indeterminate higher-order equations Narayana has also made contributions to the topic of cyclic quadrilaterals.
Proof of the theorem. We need to prove that AF = FD.We will prove that both AF and FD are in fact equal to FM.. To prove that AF = FM, first note that the angles FAM and CBM are equal, because they are inscribed angles that intercept the same arc of the circle (CD).
A rhombus is a tangential quadrilateral. [10] That is, it has an inscribed circle that is tangent to all four sides. A rhombus. Each angle marked with a black dot is a right angle. The height h is the perpendicular distance between any two non-adjacent sides, which equals the diameter of the circle inscribed.
Tangential quadrilaterals are a special case of tangential polygons. Other less frequently used names for this class of quadrilaterals are inscriptable quadrilateral, inscriptible quadrilateral, inscribable quadrilateral, circumcyclic quadrilateral, and co-cyclic quadrilateral.
Hutton's definitions in 1795 [8] The ancient Greek mathematician Euclid defined five types of quadrilateral, of which four had two sets of parallel sides (known in English as square, rectangle, rhombus and rhomboid) and the last did not have two sets of parallel sides – a τραπέζια ( trapezia [ 9 ] literally 'table', itself from ...