Derousseau's Generalization of the Malfatti circles

Angle Bisectors


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\(\mathbf{4c}\)   \((310)\)

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

Hiroyasu Kamo