QCM de géométrie

1.
Soient A, H et B trois points alignés tel que AH=a et HB=b, M un point du cercle de diamètre [AB] dont le projeté orthogonal sur (AB) est le point H. On note MH=h et on a alors:

 
 
 
 

2.
Soient A et B deux points du plan tels que AB=4.
L’ensemble des points M tel que MA^2-MB^2=16 est:

 
 
 
 

3.
Soit \mathcal{C} un cercle de centre O et de rayon R, M un point extérieur au cercle situé à une distance d de O et \Delta une droite passant par M et coupant le cercle en A et B.
Le produit \overline{MA}\times \overline{MB} est égal à:

 
 
 
 

4.
La droite passant par A(1~;~3~;~7) et orthogonale à la droite \Delta d’équation \left\{\begin{array}{cl} x& =t+5\\ y&=-4t-1\\ z&=t+3\\ \end{array}\right. a pour équation:

 
 
 
 

5.
Soit ABC un triangle et D le point d’intersection de [BC] avec la bissectrice de l’angle \widehat{BAC}.
Laquelle de ces égalités est correcte ?

 
 
 
 

6.

Soient A et B deux points tels que AB=4 et I le milieu de [AB].

L’ensemble des points M tels que  \overrightarrow{MA}.\overrightarrow{MB}=5 est :

 
 
 
 

7.

Les droites d_1 et d_2 d’équations respectives
\left\{\begin{array}{cl} x& =3t-2\\ y&=6t\\ z&=6t+3\\ \end{array}\right. et \left\{\begin{array}{cl} x& =-t-2\\ y&=5t+7\\ z&=-3t+2\\ \end{array}\right. sont:

 
 
 
 

8.
Soient A et B deux points distincts de l’espace et I le milieu de [AB].
Pour tout point M de l’espace, on a :

 
 
 
 

9.
Dans un octogone régulier inscrit dans un cercle de rayon R, la longueur de chaque côté est:

 
 
 
 

10.
Deux points C et D sont conjugués harmoniquement par rapport aux points A et B si et seulement si \dfrac{CA}{CB}=\dfrac{DA}{DB},
on a alors:

 
 
 
 

Question 1 sur 10

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