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Question
Let ABC be a triangle and D, E, F are points on the respective sides AB, BC, AC or their extensions. Let AD : DB = 5 : 3, BE : EC = 3 : 2 and AC = 21 . Find the length of the line segment CF
Solution
`"AD"/"DB" = 5/3, "BE"/"EC" = 3/2`, AC = 21
By Ceva’s theorem
`"BE"/"EC" xx "CF"/"FA" xx "AD"/"DB"` = 1
`3/2 xx "CF"/(21 - "CF") xx 5/3` = 1
`(5"CF")/(2(21 - "CF"))` = 1
`"CF"/(21 - "CF") = 2/5`
5CF = 42 – 2CF
7CF = 42
CF = `42/7` = 6
Length of the line segment CF = 6 units
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