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Prove that the angle between internal bi...

Prove that the angle between internal bisector of one base angle and the external bisector of the other base angle of a triangle is equal to one half of the vertical angle.

Text Solution

Verified by Experts

To prove- `/_E=1/2/_A`
By exterior angle theorem
`/_A+/_B=/_ACD`
`1/2/_A+1/2/_B=1/2/_ACD`
`1/2/_A+/_1=/_2`
`/_2=/_1+1/2/_A-(1)`
`In /_\BCE`
`/_ECD=/_1+/_E`
...
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