Egalitate in tetraedru

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Claudiu Mindrila
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Egalitate in tetraedru

Post by Claudiu Mindrila »

Fie \( ABCD \) un tetraedru in care \( A^{\prime},\ B^{\prime},\ C^{\prime},\ D^{\prime} \) sunt picioarele inaltimilor din varfurile \( A,\ B,\ C \) respectiv \( D \), iar cu \( \alpha,\ \beta,\ \gamma,\ \delta \) planele opuse acelorasi varfuri. Demonstrati ca daca \( AB \) si \( CD \) nu sunt perpendiculare, atunci \( CD\cdot\text{dist}\left(AA^{\prime},\ BB^{\prime}\right)=AB\cdot\text{dist}\left(CC^{\prime},\ DD^{\prime}\right) \).

Mihai Miculita, Revista Minus 1/2008
elev, clasa a X-a, C. N. "C-tin Carabella", Targoviste
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