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An Unusual Approach to Circular Inversion
Šebek, Jakub ; Škorpilová, Martina (advisor) ; Boček, Leo (referee)
This bachelor thesis aims to present the topic of circular inversion in a closer way to the non-standard knowledge of high school students actively competing in Mathematical Olympiads. The first chapter describes the topic of antiparallel lines, a relatively common knowledge among such students. The second chapter introduces an antiparallel mapping which is actually a circular inversion, but deduced solely from the properties of antiparallel lines. We consider this way of introduction to be original and closer to the principle of solving more complex olympiad problems using circular inversion. In the following two chapters the topics of power of a point and cross ratio are described and their connection to antiparallel map is shown. In those chapters the circular inversion itself is also introduced and many of its properties are proven. In the last chapter, we solve the Problem of Apollonius and prove the Feuerbach's theorem using inversion. 1

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