Ioannis Holfeld's [url=http://home.pf.jcu.cz/~hasek/Holfeld/Problem_35.pdf]Exercitationes Geometricae[/url] (1773, Prague) introduced the following problem:[br][br]Given a circle with center A and circumpoint M, radius r. Let B another circumpoint and C a point on line AB. What is the locus of points C such that MO/AO=r/BC?[br][br]Holfeld's solution was a parabola, shown below, but by using modern algebraic geometry methods and automatic computations another solution will also be delivered. Notably, a pretzel curve.

(For the details see R. Hašek, J. Zahradník: [url=http://csgg.cz/33lomna/sbornik2013.pdf]Contemporary interpretation of selected historical problems on loci[/url]. [i]Proceeding of the 33rd Conference on Geometry and Graphics.[/i] Horní Lomná, September 9–12, 2013. See also R. Hašek, Z. Kovács, J. Zahradník: Loci problems in Age of Reason and their effect on GeoGebra: [url=https://www.researchgate.net/publication/310425863_Loci_problems_in_Age_of_Reason_and_their_effect_on_GeoGebra_GeoGebra%27s_contribution_to_solving_loci_problems]GeoGebra's contribution to solving loci problems[/url], [url=https://www.researchgate.net/publication/288975684_Loci_problems_in_Age_of_Reason_and_their_effect_on_GeoGebra_Locus_equations_and_their_factorization_in_GeoGebra]Locus equations and their factorization in GeoGebra[/url], presentations at the International GeoGebra Conference, Budapest, January 24, 2014.)[br][br]The pretzel curve is introduced because by using computational algebraic geometry we cannot prescribe the exact position of point C: it can be on different rays on the line AB.[br][br]In this applet we used GeoGebra's [b]LocusEquation[/b] command. By right-clicking on the red curve, the exact syntax of the command can be read off.