## A regular pentagon and anti-pentagon

In this interactive diagram we have the pentagon case of what we had for triangles in the previous diagram. It may be helpful to have seen that demonstration first. There are a red circle and an inscribed regular pentagon s, a blue circle and an inscribed regular anti-pentagon a (with reversed orientation), red and blue radius control points, green midpoints r between corresponding red and blue ones, and green lines making up the convex pentagon that results from the construction. The radius controls and the points s0 and a0 are all draggable (as in the triangle case).

Initially the r points are all in a straight line, with a double point of r1 and r4 at the left, r2 and r3 in the middle, and the single r0 at the right. Rotating a0 a little bit splits the double points and makes the situation easier to see. The r points remain in a line until the radii of the red and blue circles differ. The resulting green figure is always an affine image of a regular pentagon, or of its reverse (when the red radius is smaller than the blue).

Turning on [Tracing] by clicking it leaves a trail of yellow dots marking where r0 has been as the mechanism is moved. Unfortunately, the only way to turn tracing off is to refresh the page and restore the applet to its start.