Question

Fie ABCD un dreptunghi. Pe laturile (AB) si (BC) se considera punctele M si N , astfel incat $\frac{AM}{AB}$ $\frac{AM}{AB} = \frac{1}{4} si \frac{BN}{NC} = 3$
a) Aratati ca MN ║ AC
b) Daca MN ∩ DB = { P } , calculati BP supra PD

VREAU SI DESENUL

Answer 1

AM/AB=1/4 (1)
BN/NC=3⇒NC/NB=1/3⇒NC/(NC+NB)= 1/(1+3)=1/4 (2)

din (1) si (2) TReciproca Teo Thales⇒MN||AC, cerinta

b) fie BD∩AC={O}
BP/BO=MB/BA=3/4

Pt ca AM/AB=1/4, ⇒AM/MB=1/3, MB/AM=3/1, MB/AB=3/4

deci BP/BO=MB/BO=3/4
cum BO=BD/2⇒BP/BD=3/8