Holditch's theorem

[url=https://en.wikipedia.org/wiki/Holditch%27s_theorem]Holditch's theorem[/url][br][br]See also the [url=https://www.geogebra.org/m/RScgNz6J]worksheet[/url] of Georg Wengler who used an ellipse.[br][br]I used an arbitrary polar function to define a convex closed curve:[br]R(φ)=0.9 + 0.1cos(2φ) + 0.02 (cos(3φ) - sin(5φ))[br]You can't intersect a parametric curve with a circle as Wengler did with his ellips.[br][br]The distance of two points on convex closed curve must be equal to the length of the chord[br]So:  Qφ(x)=(cos(φ+x)*R(φ+x)-cos(φ)*R(φ))² + (sin(φ+x)*R(φ+x) - sin(φ)*R(φ))² - (r+s)²  = 0[br][br]I used the CAS Root function to find the chord: δ:=x(Root[Qφ, 0,pi])[br][br]As far as I know you can't draw a locus of this solution in GeoGebra.[br]So I used a trace to draw the enclosed area.[br]Is there a better way to do this in GeoGebra? I really do not know.[br][br][br]

Information: Holditch's theorem