1. a) Les points R, M et O ainsi que R, N et I sont alignés dans cet ordre
et (MN) // (IO)
d'après le théorème de Thalès
RN/RI = RM/RO = MN/IO
RN/7 = x/8 = MN/3
donc
RN = 7x/8
MN = 3x/8
b) P1 = RN + NM + RM
P1 = 7x/8 +3x/8 + x
P1 = 7x/8 + 3x/8 + 8x/8
P1 = (7x+3x+8x) /8
P1 = 18x/8
P1 = x*9*2/4*2
P1 = (9/4)x
2) P2 = MN + NI + IO + Mo
MN = 3x/8
NI = RI -RN = 7-7x/8
IO = 3
MO = RO-RM = 8-x
P2 = (3x/8) + 7-(7x/8) + 3 + 8-x
P2 = (3x/8) -(7x/8) -x +7+3+8
P2 =((3x-7x-8x)/8) + 18
P2 = (-12x/8) +18
P2 = 18 - x(3*4)/(2*4)
P2 = 18 - (3/2)x
2. P1 = P2
(9/4)x = 18 - (3/2)x
(9/4)x + (3/2)x = 18
(9/4)x + (6/4)x = 18
x(9+6)/4 = 18
15x = 18*4
x = 72/15 = 4,8
