Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{7a}\) \((233)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.041196100146&{}:{}&-0.017063983397&{}:{}&-0.024132116749&,\\B^\prime&{}\approx{}&2.513669746063&{}:{}&2.041196100146&{}:{}&-3.554865846209&,\\C^\prime&{}\approx{}&0.806562964876&{}:{}&-0.806562964876&{}:{}&1.000000000000&. \end{alignedat} \]
7a (233)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-0.024132116749\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}-3.554865846209\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}-1.140652283836\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.707106781187&{}:{}&0.707106781187&{}:{}&1.000000000000&. \end{alignedat} \]
7a (233)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&1.133932084180&{}:{}&-0.062426032111&{}:{}&-0.071506052069&. \end{alignedat} \]
7a (233)

Hiroyasu Kamo