Derousseau's Generalization of the Malfatti circles

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

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

\(\mathbf{0b}\) \((101)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.876655225327&{}:{}&-0.199576037755&{}:{}&0.322920812428&,\\B^\prime&{}\approx{}&0.839915207551&{}:{}&-1.198926561037&{}:{}&1.359011353486&,\\C^\prime&{}\approx{}&0.338909579091&{}:{}&-0.338909579091&{}:{}&1.000000000000&. \end{alignedat} \]
0b (101)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.322920812428\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}1.359011353486\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}0.548367218082\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.618033988750&{}:{}&-0.618033988750&{}:{}&1.000000000000&. \end{alignedat} \]
0b (101)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.666714164514&{}:{}&-0.447316704796&{}:{}&0.780602540282&. \end{alignedat} \]
0b (101)

Hiroyasu Kamo