Problems for Moscow School 57 Students and Applicants

These problems were offered to students and applicants to Moscow School #57 (where I studied). They combine algebra and geometry and are rather interesting and often non-trivial, although they do not require any substantial knowledge beyond the standard Russian middle-school math curriculum and known even to riggers in Russia and in Chicago. I also do Algebra.

Here is the Postscript version of these problems, in Russian.