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In the adjoining figure, AD bisects angl...

In the adjoining figure, AD bisects `angleA`. Arrange AB, BD and DC in the descending order of their lengths.

Text Solution

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In `DeltaABC`
`angleBAC=180^(@)-angleABC-angleACB`
`=180^(@)-60^(@)-40^(@)=80^(@)`
`:. angleBAD=angleCAD=1/2 angleBAC =1/2 xx80^(@)=40^(@)`
In `DeltaABD`
`angleADB=180^(@)-angleABD-angleBAD`
`=180^(@)-60^(@)-40^(@)=80^(@)`
In `DeltaACD`
`angleCAD=angle ACD`
`implies" "CD=AD` ...(1)
In `DeltaABD`
`angleADB gt angle ABD gt angle BAD`
`implies" "AB gt AD gt BD`
`implies" "AB gt CD gt BD` [from (1)]
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