Equilateral Triangle in Two Congruent Circles
If we create two congruent circles, where the center point of one circle lies on the perimeter of the other and visa versa, then there exists and equilateral triangle in the shared area of the circles. You'll see this equilateral triangle (pink) in the diagram. Play with the sliders and see that no matter the size of the circles, as long as they are congruent, we will be able to construct an equilateral triangle with them.
Try this on your own to see if you can construct an equilateral triangle as we did here. What happens if a and b are set equal to the same number?