Impossible Triangles
This applet allows you to see why certain triangles are 'possible' and why certain triangles are 'impossible'.
Use the black slider to adjust the length of the base side, and the other two sliders to adjust the other two sides.
When the 'Magic' checkbox is checked, you can see the circles drawn in. You will notice that when they intersect, the point of intersection is precisely the point that joins the two other sides of a triangle. However, if the two circles do not intersect, then the triangle is impossible to construct.