Derousseau's Generalization of the Malfatti circles

\(A=30\degree\), \(B=30\degree\), \(C=120\degree\).


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

\(\mathbf{3a}\) \((033)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.247582480175&{}:{}&0.275403926508&{}:{}&0.477013593316&,\\B^\prime&{}\approx{}&-2.258531589634&{}:{}&-0.653359874111&{}:{}&3.911891463745&,\\C^\prime&{}\approx{}&-0.027821446333&{}:{}&0.027821446333&{}:{}&1.000000000000&. \end{alignedat} \]
3a (033)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.477013593316\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}3.911891463745\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}0.048188158589\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.577350269190&{}:{}&0.577350269190&{}:{}&1.000000000000&. \end{alignedat} \]
3a (033)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.036943566834&{}:{}&0.097989987026&{}:{}&0.938953579808&. \end{alignedat} \]
3a (033)

Hiroyasu Kamo