This work contains a collection of less common, more demanding
or olympiad problems from the part of planimetry, where metric
relations are used. The reader can also find here a compendium
of the theory necessary for solving such problems somewhat
extended for more curious or gifted students. We hope that
reading this work will contribute to better preparation for
mathematical competitions or for deeping student's knowledge
and skills in this area. The text can also be helpful for high
school mathematics teachers, who would like to give their
students some harder problems to solve.