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Question
D and E are points on the sides AB and AC respectively of a ΔABC such that DE║BC. Find the value of x, when
AD = x cm, DB = (x – 2) cm, AE = (x + 2) cm and EC = (x – 1) cm.
Solution
In Δ ABC, it is given that DE || BC.
Applying Thales’ theorem, we have :
`(AD)/(DB) = (AE)/(EC)`
⟹ `X/(X-2) = (X+2)/(X-1)`
⟹ `X (X-1) = (X-2) (X +2)`
⟹`X^2 - X = X^2 - 4`
⟹ X = 4 CM
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