Among other things, LibraryMan wrote:

> I am trying to figure out, because my geometry is weak, how to create a
> Gothic trefoil design (http://www.newyorkcarver.com/geometry/Trifoil.htm)
> fitting "comfortably" within another equilateral arch
> (http://www.newyorkcarver.com/geometry/equilarch.htm).
> 
> Or, put another way, how to fit three mutually equidistant congruent
> circles such that each circle is tangent to two adjacent sides of an
> equilateral triangle.
> Maybe someone could help me express the numeric relationships based on an
> eq. triangle with one side = "x"?


- Circles with radius R.
- Centers of circles form a equilateral triangle ABC of side L
- All 3 circles are tangent to a "circumscribed" triangle abc of side l
- Circle centered in A touches abc in P and Q.
- aPA is a triangle with angles of 30, 90 and 60 degrees, one leg (PA) is R, 
the other leg (aP) should be easy to calculate: sin(30)/R=sin(60)/aP
- The outer's triangle side (ab) is: aP+AB+Sb = 2*aP+L
- The relationship between R and L should be easy too: sin(60)=L/(2*R)
- I may be mistaken.

-- 
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