On some classical constructions extended to hyperbolic geometry

Matematicheskoe prosveshenie. Tret'ya seriya, 2009, N. 13 pp. 155-170 (in Russian) We consider some constructions in hyperbolic geometry that are analogous to classical constructions in Euclidean geometry. We show that both Monge's theorem and the theorem on the concurrence of the common chords of three circles also hold in absolute geometry. We proffer analogues of the Euler line and the Euler nine-point circle and also extend Feuerbach's famous theorem.