Pretty Petals

I was appreciating the geometrydaily:

#332 Totem – A new minimal geometric composition each day

And got to noticing the always neat equliateral triangle proportions in the circle where the side length is the radius. So I have to fire up GeoGebra and start playing.

I got fascinated by the lenses formed by the circular arcs trapped by the triangles, and started wondering about tangential lenses in osculating congruent circles. (Petals, I was thinking. Pretty petals.) This is the special case when the cutting chord is a radius. So I made a sketch to play with lenses of different length.



Now I'm quite curious about those special lengths of the petals. Here's the sketch if you'd like to play with it:  teacher's page (download) and student's page (applet).

Other GeoGebra inspired by Geometry Daily:

• Folding Paper
• Polychron