Réponse :
Explications étape par étape
Bonsoir
CF/FD = EF/FB = CE/BD
CF/(12 - CF) = (15 - CE)/FB = CE/9
CE/EA = EF/EB = CF/AB
CE/15 = EC/EB = CF/AB
=> CE/15 = CE/EB
EB/15 = CE/CE = 1
EB = 15 cm
CF/(12 - CF) = (15 - CE)/FB = CE/9
=> (15 - CE)/(EB - EF) = CE/9
9(15 - CE) = CE(15 - CE)
135 - 9CE = 15CE - CE^2
CE^2 - 24CE + 135 = 0
[tex]\Delta = (-24)^{2} - 4 * 1 * 135 = 576 - 540 = 36[/tex]
[tex]\sqrt{\Delta} = 6[/tex]
CE_1 = (24 - 6)/2 = 18/2 = 9 cm
CE_2 = (24 + 6)/2 = 30/2 = 15 cm
CF/(12 - CF) = CE/9
9CF = CE(12 - CF)
Soit : CE = 9 cm
9CF + 12CF = 12CE
21CF = 12CE
21CF = 12 x 9 = 108
CF = 108/21
CF ~ 5,14 cm
Soit CE = 15 cm
21CF = 12 x 15 = 180
CF ~ 180/21
CF ~ 8,57 cm
