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Question
ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that `("AO")/("BO") = ("CO")/("DO")`
Solution
Draw a line EF through point O, such that EF || CD
In ΔADC, EO || CD
By using basic proportionality theorem, we obtain
`("AE")/("ED") = ("AO")/("OC")` ...(1)
In ΔABD, OE || AB
So, by using basic proportionality theorem, we obtain
`("ED")/("AE") = ("OD")/("BO")`
⇒ `("AE")/("ED") = ("BO")/("OD")` ...(2)
From equations (1) and (2), we obtain
⇒ `("AO")/("OC") = ("BO")/("OD")`
⇒ `("AO")/("BO") = ("OC")/("OD")`
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