What are the same in triangle ABC and triangle XYZ?
Drag point B to see how the inscribed angle affects the length of the third side.
Drag point B to make [math]\angle[/math]A > [math]\angle[/math]X. Compare side [i]BC[/i] with side [i]YZ.[/i]
Drag point B to make [math]\angle[/math]A<[math]\angle[/math]X. Now compare side [i]BC [/i]with side [i]YZ[/i].