Derousseau's Generalization of the Malfatti circles

Angle Bisectors (1)


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

\(\mathbf{2}\) \((020)\)

\[\begin{aligned}\overrightarrow{AA^{\prime}}&=\dfrac{\left(1+\cot\dfrac{B}{4}\right)\left(1-\tan\dfrac{C}{4}\right)}{2\left(1-\tan\dfrac{A}{4}\right)}\overrightarrow{AI},\\\overrightarrow{BB^{\prime}}&=\dfrac{\left(1-\tan\dfrac{A}{4}\right)\left(1-\tan\dfrac{C}{4}\right)}{2\left(1+\cot\dfrac{B}{4}\right)}\overrightarrow{BI},\\\overrightarrow{CC^{\prime}}&=\dfrac{\left(1-\tan\dfrac{A}{4}\right)\left(1+\cot\dfrac{B}{4}\right)}{2\left(1-\tan\dfrac{C}{4}\right)}\overrightarrow{CI}.\end{aligned}\]

Hiroyasu Kamo