In this book, which is the second in the series Geometry for Competitions, we discuss Metric Geometry. More specifically, the material is divided into 8 sections:

- The first section contains Thales' theorem, similar triangles, bisector theorems, and the basic theorems of the bundle of lines.

- The second section covers the metric relationships of right and arbitrary triangles, the metric relationships in the circle, and includes a brief mention of the radical axis and the radical center.

- The third section explores areas, presenting various methods for calculating the area of planar shapes, and through numerous exercises, showcases their diverse use in solving complex proof and calculation problems.

- The fourth section presents regular polygons and the measurement of circles.

- The fifth section, which is perhaps the most comprehensive, includes notable theorems that are particularly useful in tackling challenging problems, such as those found in competitions and Olympiads. Among these theorems, we mention in particular Menelaus' theorem, Ceva's theorem, Leibniz's theorem, Carnot's theorem, Pascal's theorem, Ptolemy's theorem, Casey's theorem, Pappus' theorem, etc. Additionally, theorems concerning the median, the Lemoine point, the pedal triangle, Stewart's relation, Steiner's theorem, the Van Aubel relation, Apollonius' circle, as well as other useful theorems cannot be omitted.

- In the remaining sections, topics and exercises of all levels are presented, relating to national mathematical competitions from various countries, international competitions such as the Balkan Olympiad, the Baltic Way competition, the Asian Pacific Mathematical Olympiad, the International Mathematical Olympiad, etc.