Geometric principles in contest problems

This diploma thesis aims to present selected geometrical principles commonly found in contest geometry problems. The first chapter focuses on explaining the necessary basics of angle chasing and the use of circles in geometry problems. We can also find the definition of Švrček's point in the chapter, along with proofs of its basic properties. A number of basic angle chasing exercises are also provided for the reader. In the second chapter the thesis presents several methods for using similar triangles in contest pro- blems and introduces the reader to the concept of the power of a point. The last chapter is dedicated to the relatively unknown mapping of spiral similarity, providing a taste of more advanced contest geometry. Each chapter contains carefully chosen exercises re- lated to the respective topics, along with their solutions. 1