About the book

This is a translation from the revised edition of the Russian book which was issued in 1982. It is actually the first in a two-volume work on solving problems in geometry, the second volume “Problems in Solid Geometry” having been published in English first by Mir Publishers in 1986. Both volumes are designed for schoolchildren and
teachers.

This is a unique collection of interesting and elegant problems presenting the subject in a manner comprehensible to a youthful mind making it both interesting and usefulthrough a wide range of practical applications. Although the problems in this collection vary in “age” (some of them can be found in old books and journals, others were offered at mathematical olympiads or published in the journal “Quant” (Moscow, we still hope that some of the problems in the collection will be of interest to experienced geometers.

Almost every problem is non-standard (as compared with routine exercises on solving equations, inequalities, etc.): one has to think of what additional constructions must be made, or which formulas and theorems must be used. Therefore, this collection cannot be regarded as a problem hook in geometry; it is rather a collection of geometrical puzzles aimed at demonstrating the elegance of elementary geometrical techniques of proof and methods of computation (without using vector algebra and with a minimal use of the method of coordinates, geometrical transformations, though a somewhat wider use of trigonometry).