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O is any point in the interior of DeltaA...

O is any point in the interior of `DeltaABC`. Bisectors of `/_AOB, BOC` and AOC intersect sideAB, side BC, side AC in F,D and E respectively.
Prove that `BFxxAExxCD=AFxxCExxBD`.

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In `Delta AOB,`
ray OF bisects `angle AOB" "` ...(Given)
` (AO)/(OB) = (AF)/(FB)" "` …(By theorem of angle bisector of trinagle ) … (1)
In `Delta BOC`
ray OD bisects `angle BOC " "` … (Given)
`(OB)/(OC)= (BD)/(DC) " "` ...(By theorem of angle bisector of Delta ) ...(2)
In ` Delta AOC,`
ray OE bisects ` angle AOC" "` ... (Given)
`(OC)/(OA) = (CE)/(AE)" "` ...(By theorem of angle bisector of Delta ) ...(3)
Multiplying (1),(2),(3) , we get
` (AO)/(OB) xx (OB)/(OC) xx (OC)/(OA) = (AF)/(FB) xx (BD)/(DC) xx (CE)/(AE)`
` :. 1 = (AF)/(FB) xx (BD)/(DC) xx (CE)/(AE)`
` :. AF xx BD xx CE = BF xx AE xx CD`
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NAVNEET PUBLICATION - MAHARASHTRA BOARD-CHALLENGING QUESTIONS-SECTION 3 (MODEL QUESTION PAPER FOR PRACTICE ) Solve any one of the following subquestions :
  1. O is any point in the interior of DeltaABC. Bisectors of /AOB, BOC and...

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  2. Solve any one of the following subquestions : Draw a circle with c...

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