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If D any point on the BC of an isosceles...

If D any point on the BC of an isosceles triangle ABC then prove that `AB gt AD` and `AC gt AD`.

Text Solution

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In `DeltaABC`
`AB=AC`
`implies" "angleACB=angleABC` ...(1)
In `DeltaABD`
`angleADC=angleABD + angle BAD" "( angleADC" is exterior angle")`
`implies" "angleADC gt angleABD`
`implies" "angleADC gt angleACD` [from (1)]
`implies" "Ac gt AD` Hence Proved.
Again in `DeltaACD`
`angleADB=angleACD+angleCAD" "(angleADB" is exterior angle")`
`implies" "angleADB gt angleACD`
`implies" "angleADB gt angleABD` [from (1)]
`implies" "AB gt AD` Hence Proved.
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