Triunghi si arie constanta

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Filip Chindea
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Joined: Thu Sep 27, 2007 9:01 pm
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Triunghi si arie constanta

Post by Filip Chindea »

Fie \( ABC \) un triunghi si \( A_1B_1C_1 \) triunghiul median, \( A_1 \in BC \). Fie \( P \) variabil pe cercul circumscris. Dreptele \( PA_1, PB_1, PC_1 \) taie cercul din nou in \( A^{\prime}, B^{\prime}, C^{\prime} \), respectiv. Presupunem ca \( A, B, C, A^{\prime}, B^{\prime}, C^{\prime} \) sunt distincte iar \( AA^{\prime}, BB^{\prime}, CC^{\prime} \) determina un triunghi. Sa se arate ca aria acestuia nu depinde de \( P \).

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