This paper discusses characterizations of cyclic quadrilaterals. A cyclic quadrilateral is planar geometric object, whose vertices all lie on the same circle. The thesis describes and proves the basic theorems as well as some less known characterizations. All theorems are accompanied by proofs and proofs of converse. Those usually contain properties of similar triangles and congruent angles. For the proofs in this paper it is also necessary to understand the inscribed angle theorem. Paper takes a deeper look at the old Japanese theorem about cyclic polygons. For the first time it is possible to read the direct proof of the theorem and the proof of converse in the same place.
|
