Derousseau's Generalization of the Malfatti circles

\(a:b:c=5:12:13\).

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

\(\mathbf{7b}\) \((323)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.623827207244&{}:{}&7.485926486933&{}:{}&-8.109753694177&,\\B^\prime&{}\approx{}&-0.019099492400&{}:{}&1.068758172640&{}:{}&-0.049658680240&,\\C^\prime&{}\approx{}&-0.295152490866&{}:{}&0.708365978077&{}:{}&0.586786512788&. \end{alignedat} \]
7b (323)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-3.742963243466\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}-0.022919390880\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}-0.354182989039\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.833333333333&{}:{}&-2.000000000000&{}:{}&2.166666666667&. \end{alignedat} \]
7b (323)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.070073392212&{}:{}&1.197728780605&{}:{}&-0.127655388392&. \end{alignedat} \]
7b (323)

Hiroyasu Kamo