problema 1
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A M B P N C
M mijlocul lui AB => AM = MB = [tex] \frac{AB}{2} [/tex]
N mijlocul lui BC => BN = NC = [tex] \frac{BC}{2} [/tex]
P mijlocul lui AC => AP = PC = [tex] \frac{AC}{2} [/tex]
AB = 2 * AM = 2 * 5 = 10
BC = MC - MB => BC = 11 - 5 = 6
AC = AB + BC => AC = 10+6 - 16
NC = BN = [tex] \frac{BC}{2} [/tex] = [tex] \frac{6}{2} [/tex] = 3
AP = PC = [tex] \frac{AC}{2} = \frac{16}{2} = 8[/tex]
NP = 8-5 = 3
problema 2
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A O B M
AO = OB = AB / 2
OM = OB + BM
2OM=2 (OB + BM) = 2OB + 2BM = AB + 2BM
MA = BA + MB
MB = MB
=> 2 OM = MA + MB
Problema 3
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A B C D
AB = AB
AD = AB + BD = AB + 64
AB + AD = AB + AB + 64 = 2AB + 64
2AC = 2AB + 64 ( SE IMPARTE LA 2 ) = > AC = AB + 32
AB + BC = AC
DIN ULTIMELE DOUA RELATII => 32 + AB = AB + BC ( SE ELIMINA AB) =>
BC = 32
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