ABCD is a trapezium in which AB||DC and its diagonals intersect each o – InterviewSolution

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1.	ABCD is a trapezium in which AB\|\|DC and its diagonals intersect each other at the point O. Show that `(A O)/(B O)=(C O)/(D O)`.
Answer» `In/_ACD` EO\|\|DC `(AE)/(ED)=(AO)/(OC)`-(1) `In/_BCD` OF\|\|DC `(BO)/(OD)=(BF)/(FC)` `In/_ADB` EO\|\|AB `(EA)/(DE)=(OB)/(OD)` putting this value in equation 1 `(OC)/(OB)((AO)/(OC)=(OB)/(OD))(OC)/(OB)` `(AO)/(OB)=(OC)/(OD)`

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