Derousseau's Generalization of the Malfatti circles

Angle Bisectors (1)


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

\(\mathbf{2a}\) \((031)\)

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

Hiroyasu Kamo