Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{5a}\) \((213)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.334089318960&{}:{}&-0.138384326957&{}:{}&-0.195704992003&,\\B^\prime&{}\approx{}&1.806562964876&{}:{}&1.748302881333&{}:{}&-2.554865846209&,\\C^\prime&{}\approx{}&2.513669746063&{}:{}&-2.513669746063&{}:{}&1.000000000000&. \end{alignedat} \]
5a (213)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-0.195704992003\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}-2.554865846209\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}-3.554865846209\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.707106781187&{}:{}&0.707106781187&{}:{}&1.000000000000&. \end{alignedat} \]
5a (213)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&1.731886145206&{}:{}&-0.095345022530&{}:{}&-0.636541122676&. \end{alignedat} \]
5a (213)

Hiroyasu Kamo