|Autors: Nenkov, VN., Ivanov, YN., Velchev, A. P., Stefanov, ST.|
Title: More on the Inscribed Quadrilateral
Keywords: Inscribed Quadrilateral
Abstract: In the first part of the article, using appropriate problems, are considered various structures in the plane, containing a quadrilateral, which is proved to be inscribed. Proofs are made via known in geometry classes in eighth class criteria, when a quadrilateral is inscribed. The second part deals with applications of properties of an inscribed quadrilateral to solve different geometric problems. One of them is about the well-known property of the images symmetric of triangle’s orthocentre with respect to its sides and their midpoints. Another considered problem is the statement of the well-known Mikel’s theorem for a triangle, and one of the following problems is of increased difficulty and it is authorial. The third part of the article discusses popular properties of the inscribed quadrilateral. Two of them, related to the angle bisectors at the angles between the extensions of every couple of opposite sides of cyclic tetragon, are highly interesting.
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