Cercuri tangente si omotetie

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Filip Chindea
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Joined: Thu Sep 27, 2007 9:01 pm
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Cercuri tangente si omotetie

Post by Filip Chindea »

Fie \( ABCD \) convex si \( \gamma_B \), \( \gamma_D \) cercurile inscrise in triunghiurile \( ABC \), \( ADC \), respectiv. Aratati ca punctele de tangenta ale \( \gamma_B, \gamma_D \) la \( [AC] \) sunt simetrice fata de mijlocul acestei diagonale daca si numai daca \( AC, BD \) si dreapta trecand prin centrele celor doua cercuri sunt concurente.

[ Stelele Matematicii 2008 - Problema 3 ]
Life is complex: it has real and imaginary components.
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