[size=150]The applet below is a self exploration of Geogebra's PathParameter variable which allows points to be located on geometrical objects via values from 0 to 1. [br][br]The study below is about PathParameter values of a Point on a Circle.[br]In applying the observations of 3 points P, Q and R and some manipulation, the applet[br][br]1. Generates triangles using one free point, P and either specified angles at vertices Q, R, or [br]2. Randomly autogenerate PathParameters for P, Q, and R, many possible triangles can be drawn .(Here only equilateral triangles in different orientations were prepared)[br][br]Future study would include generating valid triangles based on other constraints, and they would rely on understanding the properties of congruency of triangles, ie SSS, SAS, AAS, RHS etc.[br][br][/size]Others' pathparameter studies (eg. by  [url=https://www.geogebra.org/usi_desu]usi_desu[/url]) [br][url=https://www.geogebra.org/m/u6MCqGQu]PathParameter of Point on line (function/formula)[/url][br][url=https://www.geogebra.org/m/Dgy9GNeT]PathParameter of Point on segment (function/formula)[/url][br][url=https://www.geogebra.org/m/kzW8SKGm]PathParameter of Point on Circle (function/formula)[/url][br][url=https://www.geogebra.org/m/Hka7sU5u]PathParameter of Point on  Ellipse (function/formula)[/url][br][url=https://www.geogebra.org/m/u6MCqGQu]PathParameter  How to Calculate[/url][br]