We have already studied the deltoid, an aesthetically pleasing figure with three curved sides, centred at the origin O. The origin is then a natural choice to take as the centre of inversion. We choose the incircle of the deltoid as the circle of inversion, but any circle with O as centre will do.

Click the linked figure below, and then click the ‘Animate’ button to generate the inverse of the deltoid. Click the button again to stop the generation. Clicking the little x at bottom right will clear the drawing from the applet window. Now slowly drag the red point around the circle. Can you explain this inverse construction? Compare the resulting inverse with the inverse of the astroid.