Réponse :
a) calcule AN et AB
th.Thalès : AB/AM = BC/MN ⇔ AB/AM = 2/6 = 1/3 ⇒ AB = 4.5/3 = 1.5
AC/AN = BC/MN ⇔ AC/AN = 1/3 ⇒ AN = 3 x AC = 3 x 3 = 9
b) calcule CT et AB
CS/CB = ST/AB ⇔ 3/AB = 5/3 ⇔ 5 x AB = 13 x 3 ⇒ AB = 13x3/5 = 7.8
CS/CB = CT/CA ⇔ CT/CA = 5/13 ⇔ CT/6.5 = 5/13 ⇒ CT = 6.5 x5/13 = 2.5
c) calcule AC et BC
AP/AB = AM/AC ⇔ 4/6 = 5/AC ⇔ 2/3 = 5/AC ⇒ AC = 15/2 = 7.5
AP/AB = PM/BC ⇔ 2/3 = 3/BC ⇒ BC = 9/2 = 4.5
d) calcule IK, MK et LK
IL/IJ = IM/IK ⇔ 8/10 = 5/IK ⇔ 4/5 = 5/IK ⇒ IK = 25/4 = 6.25
MK = IK - IM = 6.25 - 5 = 1.25
LM/JK = IL/IJ ⇔ LM/7 = 4/5 ⇒ LM = 28/5 = 5.6
Explications étape par étape
