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Se considera triunghiulMNP si punctele R∈(MN) si  Q∈(NP),astfel incat RQ||MP. Daca:a)RN=4cm,MN=10 cm,NP=15cm,calculati NQ,MR,QP.    b)NQ=7cm,MR=10cm,MN=24cm,calculatiRN,NP,QP.


Răspuns :

a) Daca RQ||MP, trebuie sa folosesti teorema lui Thales.
RQ||MP => MN/RN=PN/NQ
NQ=PN · RN/MN= 15· 4/10 =6 cm
MR=MN-NR=10-4=6 cm
QP=PN-NQ=15-6=9 cm
b) RN=MN-MR=24-10=14 cm
RQ||MP => PN/QN=MN/RN
PN= QN· MN/RN= 7· 24/14= 12 cm
QP=PN-QN=12-7=5 cm