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