Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{0a}\) \((011)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-1.513669746063&{}:{}&1.041196100146&{}:{}&1.472473645917&,\\B^\prime&{}\approx{}&-0.240108467526&{}:{}&0.900543816310&{}:{}&0.339564651216&,\\C^\prime&{}\approx{}&-0.334089318960&{}:{}&0.334089318960&{}:{}&1.000000000000&. \end{alignedat} \]
0a (011)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}1.472473645917\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}0.339564651216\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}0.472473645917\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.707106781187&{}:{}&0.707106781187&{}:{}&1.000000000000&. \end{alignedat} \]
0a (011)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.503726575887&{}:{}&0.700890186899&{}:{}&0.802836388989&. \end{alignedat} \]
0a (011)

Hiroyasu Kamo