The Limaçon as an Envelope of Circles

Let be a point and be a circle whose center is not . For any point on the circle we construct another circle with center this point and passing through . The envelope of the circles with centers on and passing through is a Limaçon.
  • Drag the slider, or click the Animation ON/OFF button to construct the circles.
  • Drag point : outside the circle , on the circle, or inside the circle, to see the changes in the Limaçon.
  • For what position of the limaçon is a dimpled,with cusp (a cardioid) or a limaçon with a loop?