In the figure below, the origin is the focus of the green parabola, and the blue unit circle ([math]r=1[/math]) is shown in blue. The inverse of the parabola with respect to the unit circle is the red cardioid. As we can see, [math]\text{|OA|}[/math] and [math]\text{|OB|}[/math] are reciprocals. So, it follows that [math]\text{|OA||OB|=r^2=1}.[/math][br][br]If you select the "Tangent line and inverse" option, you will see the tangent line to the parabola and the inverse of the tangent line. This produces a circle that is tangent to the cardioid at A. If you select the circle option, you will see that the circle's center is on the cardioid's generating circle.