if A=(1,2,3,4),B =(2,4,6,8),C=(3,4,5,6)verify that ACBC)=(AoB)o(AOC)
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given: O is the interior point of triangle ABC.
OD , OE and OF are the angle bisector of ∠AOB , ∠BOC and ∠AOC respectively.
TPT: AD*BE*CF = DB*EC*FA
proof:
in the triangle AOB, OD is the angle bisector of ∠AOB;
[since angle bisector theorem states that an angle bisector in a triangle divides the opposite side into two segments which are in the same proportion as the other two sides of the triangle.]
therefore  ..............(1)
similarly in the triangle BOC , OE is the angle bisector of ∠BOC.
therefore  ............(2)
in the triangle AOC, OF is the angle bisector of ∠AOC.
therefore  ...........(3)
from eq(1), eq(2) and eq(3):

given: O is the interior point of triangle ABC.
OD , OE and OF are the angle bisector of ∠AOB , ∠BOC and ∠AOC respectively.
TPT: AD*BE*CF = DB*EC*FA
proof:
in the triangle AOB, OD is the angle bisector of ∠AOB;
[since angle bisector theorem states that an angle bisector in a triangle divides the opposite side into two segments which are in the same proportion as the other two sides of the triangle.]
therefore  ..............(1)
similarly in the triangle BOC , OE is the angle bisector of ∠BOC.
therefore  ............(2)
in the triangle AOC, OF is the angle bisector of ∠AOC.
therefore  ...........(3)
from eq(1), eq(2) and eq(3):

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