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.