A squashed Astroid as an Envelope

In the applet below the radius of the orange circle is and the radius of the blue circle is . One point is moving clockwise along the blue circle and another point is moving counterclockwise along the orange circle. The envelope of the lines passing through these points is a squashed astroid.
  • Drag the slider to change the radius of the blue circle.
  • Show the graph of the (non-squashed) astroid.
  • What happens when the radius increases?
See more in Mathematics Magazine Vol. 82, No 3, June 2009, p. 185