Réponse :

Explications étape par étape

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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

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