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ABCD is a trapezium such that AB||CD. It...

ABCD is a trapezium such that AB||CD. Its diagonals AC and BC intersect each other at O. Prove that ` (AO)/(OC) = (BO)/(OD)`

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Draw EO||AB||CD
Now.in ` DeltaADC`, since EO||DC
` (AE)/(ED)=(AO)/(OC) ` ( by B.P theorem) ….(1)
In ` DeltaABD` , since EO||AB
`(AE)/(ED)= (BO)/(OD)` ( by B.P theorem) …(2)
From (1) and (2) , we have
`(AO)/(OC)= (BO)/(OD)`
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