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Diploma thesis deals especially with practical examples on the topic of conics. It is divided into two parts. The first part includes chapters with examples on the topics discussed in the course Geometry I. In the second part affine properties of conics, which can be used in construction tasks, Pascal's theorem and Brianchon's theorem and their use are mentioned. The aim of this thesis is to ilustrate the conics on typical examples for those interested and then to show them the interesting properties, for which there is no space in the course Geometry I.

This diploma thesis is focused on Selected problems in planimetry. The aim of this diploma thesis is description not only planimetric problems and their verification in a dynamic mathematical program GeoGebra, but also presentation of the author after whom it is called. The thesis is illustrated with pictures, which can help the reader to understand the problem and verification. This thesis can be used as a supplement the curriculum in secondary schools, where using dynamic program GeoGebra and subsequent verification may reach a better understanding of the topic.