\input zb-basic \input zb-matheduc \iteman{ZMATH 2014e.00552} \itemau{Kme\v tov\'a, M\'aria} \itemti{Minimum distance in geometric constructions. (Kon\v struk\v cn\'e \'ulohy o minim\'alnych vzdialenostiach.)} \itemso{\v{S}ediv\'y, Ondrej (ed.) et al., Slovn\'e a kon\v{s}truk\v{c}n\'e \'ulohy ako prostriedok k rozvoju logick\'eho myslenia. Nitra: Constantine The Philosopher University in Nitra, Faculty of Natural Sciences (ISBN 978-80-558-0238-1). Pr{\'\i}rodovedec 516, 35-40 (2013).} \itemab Summary: \v Cl\'anok obsahuje s\'eriu \'uloh so stup\v nuj\'ucou n\'aro\v cnost'ou na t\'emu kon\v struk\v cn\'eho hl'adania minim\'alnych vzdialenost\'\i. V rie\v sen\'\i{} \'uloh sa vyu\v zij\'u hlavne geometrick\'e transform\'acie. \itemrv{~} \itemab Summary: The article contains a series of tasks with escalating demands on the search of the minimum distance by geometric construction. When solving these problems plane geometric transformations are used mainly. \itemrv{~} \itemcc{G44 G45 G54 G55 U44 U45} \itemut{minimum distance; Fagnano's problem; Fermat's problem} \itemli{} \end