Derousseau's Generalization of the Malfatti circles

\(A=45\degree\), \(B=45\degree\), \(C=90\degree\).


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

\(\mathbf{0b}\) \((101)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.900543816310&{}:{}&-0.240108467526&{}:{}&0.339564651216&,\\B^\prime&{}\approx{}&1.041196100146&{}:{}&-1.513669746063&{}:{}&1.472473645917&,\\C^\prime&{}\approx{}&0.334089318960&{}:{}&-0.334089318960&{}:{}&1.000000000000&. \end{alignedat} \]
0b (101)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.339564651216\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}1.472473645917\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}0.472473645917\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.707106781187&{}:{}&-0.707106781187&{}:{}&1.000000000000&. \end{alignedat} \]
0b (101)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.700890186899&{}:{}&-0.503726575887&{}:{}&0.802836388989&. \end{alignedat} \]
0b (101)

Hiroyasu Kamo