Triabola
Consider the given green line and blue triangle. One might ask what curve is formed by the centers of circles tangent to both the line and triangle.
It is stitched together out of the following pieces:
1. The parabola with focus C and green line as directrix, but only up to point F
2. The portion of the angle bisector of AB and CD (extended), from F to G
3. The portion of the parabola with D as a focus, but only between G and H.
4. The portion of the angle bisector of AB and DE (extended), from H to I
5. The portion of the parabola with E as a focus, but only from I onwards
You can move the circles centered at K, M, J, N, and L (respective to the numbers above) to investigate these relationships.