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Question
An artist has created a triangular stained glass window and has one strip of small length left before completing the window. She needs to figure out the length of left out portion based on the lengths of the other sides as shown in the figure
Solution
Given that AE = 3 cm, EC = 4 cm, CD = 10 cm, DB = 3 cm, AF = 5 cm.
Let FB be x
Using Ceva’s theorem we have
`"AE"/"EC" xx "CD"/"DB" xx "BF"/"AF"` = 1
`3/4 xx 10/3 xx x/5` = 1
`(2x)/4` = 1
2x = 4 ⇒ x = `4/2` = 2
The value of BF = 2
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