Réponse :

Explications étape par étape

Bonjour

1) OM/OD = OA/OC = AM/DC

OB/OM = ON/OA = NB/AM

2) NO = 5 cm ; OA = 4 cm

OM = 3 cm ; AC = 2 cm ; CD = 3 cm

Segment BO :

OB/OM = ON/OA

OB = ON x OM / OA

OB = 5 x 3 / 4

OB = 3,75 cm

Longueur AM puis BN :

OA/OC = AM/CD

OA/(OA + AC) = AM/CD

4/(4 + 2) = AM/3

AM = 3 x 4 / 6

AM = 2 cm

OB/OM = NB/AM

NB = AM x OB / OM

NB = 2 x 3,75 / 3

NB = 2,5 cm