Rybkin's Collection of Problems in Geometry, Part I

The companion problem collection to Kiselev's classical Russian geometry — now in English for the first time.

Rybkin's Planimetry Problems is the set Russian students worked through alongside Kiselev's geometry textbook for over a century. Kiselev gives the definitions, theorems, and proofs; Rybkin gives the problems that turn those proofs into geometric intuition.

970 problems across 16 sections, organised chapter-by-chapter to mirror Kiselev's Planimetry — preliminary concepts and the straight line; angles, parallels, and adjacent constructions; triangles, with congruence, special lines, and area; parallelograms, trapezoids, and quadrilaterals; the circle, with chords, tangents, and inscribed angles; similar figures and proportional segments; numerical relations in plane figures; regular polygons and the circumference of a circle; measurement of areas — triangle, polygon, and the circle; and algebra applied to geometry. Worked solutions for the harder problems, hints for the rest.

Why this book exists.

Russian-school geometry is built on the same proof discipline that produced Markov, Kolmogorov, and their students. It taught generations of Russian mathematicians how to think geometrically — how to see a triangle as a system of relationships, not a static picture. Rybkin's Planimetry Problems is the problem set that did the teaching. 970 problems, sequenced from gentle "draw and measure" warm-ups to problems that demand the full toolkit of similar triangles, the inscribed-angle theorem, the power of a point, and the algebra of areas.

This is the first complete English translation, faithful to the original Russian edition. Every figure has been redrawn from the source; every problem has been verified against the source.

Who it is for.

Homeschool parents and tutors using a rigorous plane-geometry textbook (Kiselev, Hadamard, AoPS, or any classical alternative) who need a companion problem set with depth and variety.

Students in grades 6–9 (US) / Years 7–11 (UK) who have completed an introduction to Euclidean geometry and want substantial problem practice.

Olympiad prep groups looking for a graded source of plane-geometry problems with Russian-tradition difficulty curves.

Adult self-learners who want to revisit geometry with a clean, proof-based problem source.

What's inside.

970 problems across 16 sections, problem-numbered for easy reference; 73 figures, redrawn from the original Russian source; worked solutions for the more difficult exercises and hints for the rest; an appendix on pre-revolutionary Russian units of measure, retained where the original problems use them; and a Translator's Preface explaining the editorial choices.

Translated by Valery Manokhin, PhD (Royal Holloway, University of London) and published by Northern Star Academic Press as part of the Russian Math Books programme. The full curriculum — Kiselev's Arithmetic, Algebra Parts I and II, Planimetry, Stereometry, and Calculus, plus Rachinsky, Perelman, Markov, and Malinin & Burenin — is at russianmathbooks.com.