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Subiecte examen Politehnica 08 2000, geometrie plana, spatiu si trigonometrie

... EMBED Equation.3 d EMBED Equation.3 e EMBED Equation.3 f EMBED Equation.3 .Sa se determine EMBED Equation.3 , astfel incat EMBED Equation.3 .a nu exista b alt raspuns c EMBED Equation.3 d EMBED Equation.3 e EMBED Equation.3 f EMBED Equation.3 .In triunghiul EMBED Equation.3 , dreptunghic in EMBED Equation.3 , lungimile laturilor satisfac relatiile EMBED Equation.3 , EMBED Equation.3 . Atuncia EMBED Equation.3 b EMBED Equation.3 c EMBED Equation.3 d EMBED Equation.3 e EMBED Equation.3 f EMBED Equation.3 .Un cub ABCDA2 B2 C2 D2 se sectioneaza cu planul mediator al diagonalei AC2 . Sa se specifice forma sectiunii obtinute.a triunghi b trapez c octogon d hexagon e patrat f pentagon.Se da o coroana circulara de raze R, r Rr. Cercul mic este inscris, iar cercul mare este circumscris aceluiasi triunghi. Sa se calculeze raportul EMBED Equation.3 .Sa se calculeze produsul EMBED Equation.3 a EMBED Equation.3 b EMBED Equation.3 c EMBED Equation.3 d EMBED Equation.3 e EMBED Equation.3 f EMBED Equation.3 .Pe latura AD a paralelogramului ABCD se considera punctul E astfel incat EMBED Equation.3 Fie F punctul de intersectie al dreptei BE cu diagonala AC. Sa se calculeze raportul EMBED Equation.3 a EMBED Equation.3 b EMBED Equation.3 c EMBED Equation.3 d EMBED Equation.3 e EMBED Equation.3 f alt raspuns.Fie A si B doua puncte distincte fixate intr-un plan. Sa se determine multimea punctelor M din plan pentru care aria triunghiului MAB este constanta.o dreapta paralela cu AB b un punct c reuniunea a doua drepte concurente d un cerc trecand prin A si B e reuniunea a doua drepte paralele f o dreapta perpendiculara pe AB.In triunghiul ascutitunghic ABC, punctele C si B sunt picioarele inaltimilor duse din varfurile C si B. Se da EMBED Equation.3 si EMBED Equation.3 . Sa se calculeze BC. EMBED Equation.3 b EMBED Equation.3 c EMBED Equation.3 d nu se poate calcula e EMBED Equation.3 f EMBED Equation.3 .Fie EMBED Equation.3 lungimile laturilor unui triunghi ABC. Sa se calculeze EMBED Equation.3 daca EMBED Equation.3 si EMBED Equation.3 . EMBED Equation.3 b EMBED Equation.3 c EMBED Equation.3 d EMBED Equation.3 e EMBED Equation.3 f EMBED Equation.3 .Un tetraedru are volumul V si aria totala A. Sa se calculeze raza sferei inscrise in tetraedru. EMBED Equation.3 b EMBED Equation.3 c EMBED Equation.3 d EMBED Equation.3 e EMBED Equation.3 f EMBED Equation.3 .Un triunghi echilateral este descompus in N triunghiuri echilaterale in modul urmator fiecare latura a triunghiului dat este impartita in n parti egale si prin punctele de diviziune se duc drepte paralele cu laturile triunghiului. Sa se determine N. EMBED Equation.3 b EMBED Equation.3 c EMBED Equation.3 d EMBED Equation.3 e EMBED Equation.3 f EMBED Equation.3 .Fie VABCD o piramida patrulatera regulata cu toate muchiile de lungime EMBED Equation.3 . Sa se calculeze distanta de la mijlocul M al muchiei laterale VA la muchia BC a bazei. EMBED Equation.3 b EMBED Equation.3 c EMBED Equation.3 d EMBED Equation.3 e EMBED Equation.3 f EMBED Equation.3 .iB!-.23FGHIOPcdeflm,ajCJEHUajzUVmHajCJEHUajzUVmHa
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