Derousseau's Generalization of the Malfatti circles

\(A=36\degree\), \(B=36\degree\), \(C=108\degree\).

*
[Other solutions]
[Guy]
[Lob & Richmond]

\(\mathbf{0a}\) \((011)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-1.198926561037&{}:{}&0.839915207551&{}:{}&1.359011353486&,\\B^\prime&{}\approx{}&-0.199576037755&{}:{}&0.876655225327&{}:{}&0.322920812428&,\\C^\prime&{}\approx{}&-0.338909579091&{}:{}&0.338909579091&{}:{}&1.000000000000&. \end{alignedat} \]
0a (011)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}1.359011353486\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}0.322920812428\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}0.548367218082\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.618033988750&{}:{}&0.618033988750&{}:{}&1.000000000000&. \end{alignedat} \]
0a (011)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.447316704796&{}:{}&0.666714164514&{}:{}&0.780602540282&. \end{alignedat} \]
0a (011)

Hiroyasu Kamo