Kissing Petals

I love a tumblr called Geometry Daily that has excellent, clean geometry inspired art. One particular one related circles and equilateral triangles. (http://geometrydaily.tumblr.com/post/36666402776/332-totem-a-new-minimal-geometric-composition) That got me noticing the arcs that were formed, which got me thinking about lenses in tangential circles. Plus I love the flower petal appearance. Which petal lengths result in pretty petal arrangements? What else do you notice about the geometric relationships here?