Proof of Angle Bisector Theorem | Triangle Angle Bisector Theorem Proof

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I migh be wrong but Labeling the sides make it easier to follow up than using vertex as segment.
AB = x. AC = y that way it will not be busy during calculation. Plus it is easy for followers to remember the sides without reading the vertex

Abby-hisf
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By BPT
AB/AE = BD/DC
as AE = AC
ie, AB/AC = BD/DC

abhiamathsguide
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For me sine law or ratio of areas of this two triangles is quite easy proof

holyshit
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Sir, don't give sub titles . It is causing obstruction . We can't see what you are writing . Regards.

kaliprasadguru