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Question
In ΔABC, DE || AB. If AB = a, DE = x, BE = b and EC = c. Then x expressed in terms of a, b and c is ______.
Options
`("ac")/"b"`
`("ac")/("b" + "c")`
`("ab")/"c"`
`("ab")/("b" + "c")`
Solution
In ΔABC, DE || AB. If AB = a, DE = x, BE = b and EC = c. Then x expressed in terms of a, b and c is `underlinebb((ac)/(b + c))`
Explanation:
In ΔCDE and ΔCAB
∠C = ∠C ...[Common]
∠1 = ∠2 ...[Corresponding angles as DE || AB]
ΔCDE ∼ ΔCAB ...[By AA rule]
`("DE")/("AB") = ("CE")/("BC")` ...[Sides of similar triangles]
`x/"a" = "c"/("b" + "c")`
x = `("ac")/("b" + "c")`
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