This book is aimed at students who love Euclidean Geometry and wish for a more serious introduction and deepening of geometric concepts.

Its main purpose is to help students participating in mathematics competitions develop a substantial relationship with the subject matter and equip them with the necessary skills to successfully tackle exercises and problems at an Olympic level.

The book contains two significant sections of Geometry. The first deals with the metric relationships in the circle, which essentially is the power of a point. The second section is dedicated to the radical axis and the radical center.

At the beginning of each section, we present the relevant theorems along with their proofs, as well as a significant number of basic applications to help even lower-grade students understand these concepts.

Subsequently, we provide a substantial number of exercises of Olympic spirit, so to speak. These exercises have been designed to have escalating difficulty, aiming to capture the reader's interest and keep it sustained throughout their study. They are exercises that reach the level of international mathematics Olympiads.

For this reason, they require all the basic theorems for their solutions: from triangles, parallelograms, similarity, and cyclic quadrilaterals, thus giving the student the opportunity to enjoy how these theorems are applied in solving complex and original exercises.