Triangular Possibilities (with sliders)

Which sets of sides can make a triangle? You can use the sliders to choose the length of the sides. Then click and drag the white dots to see if you make a triangle. If the white dots get stuck on each other, just click the big button.
Can you work out a rule for which sets of sides make a triangle? I have drawn two grey circles. What do you notice about these circles? When do they intersect (overlap)?