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If a line intersects sides AB and AC of a `DeltaA B C`at D and E respectively and is parallel to BC, prove that `(A D)/(A B)=(A E)/(A C)`

Text Solution

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`/_ADE`~`/_ABC` (AAA)
`(AD)/(AB)=(DE)/(BC)=(AE)/(AC)`
`(AB)/(AD)=(AC)/(EA)`
`(AD+DB)/(AD)=(AE+EC)/(AE)`
`1+(DB)/(AD)=1+(EC)/(AC)`
`(DB)/(AD)=(EC)/(AC)`
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