Malfatti's Circles Solution from Zalgaller & Los'
Malfatti's Marble Problem asks: How can we arrange in a given triangle three non-overlapping circles of greatest area? For an Isosceles triangle, the first two circles are drawn as K1 and K2. Then we choose K3a or K3b depending on the relationship between sin(alpha) and tan(beta/2). Play around with the triangle and tell me -
- Do we use K3a or K3b when sin(alpha) > tan(beta/2)?
- Do we use K3a or K3b when sin(alpha) < tan(beta/2)?
- What do we do when sin(alpha) > tan(beta/2)?
- Also, are the three circles always symmetric for an Isosceles triangle?