A triangle [math]\Delta ABC[/math] is given. (Don't read the theorem statement in the app).[br][br]Move points [i]A[/i], [i]B[/i] and [i]C[/i] and observe how triangle [math]\Delta HGI[/math] changes accordingly.[br][br]Use GeoGebra tools to discover the common properties of points [i]H[/i], [i]G[/i] and [i]I[/i], and of triangle [math]\Delta HGI[/math], which don't depend on the position of the vertices [i]A[/i], [i]B[/i] and [i]C [/i]of the given triangle.[br][br]Formulate a conjecture about the possible [i][color=#c51414]Hypotheses[/color] [/i]and [i][color=#c51414]Thesis[/color] [/i]of the theorem that you see in the applet, then show the theorem's [i][color=#1551b5]Statement,[/color][/i] and compare them.[br][br]Explore the construction and discover the[color=#0000ff][i] Fermat's circles [/i][/color]of the sides of the triangle.