[math-fun] A Malfatti Miracle.

It's well-known to those who well know it that there are 32 Malfatti configurations (of sets of 3 circles each touching 2 others & 2 sides of a triangle). Theorem. The 32 radical centres lie in pairs on 64 lines, 16 through each of the vertices of the triangle and 4 through each of 4 other, orthocentric, points, whose (common) 9-point centre is the orthocentre of the original triangle. I have a nice description, too long for the margin of this machine, which uses Conway's extraversion and nim-addition. Three of the last 4 points are in perspective with the original triangle. I suspect that there are centres (yes, genuine Kimberling ones) that may not be in the official collection. R.