Question

if A=(1,2,3,4),B =(2,4,6,8),C=(3,4,5,6)verify that ACBC)=(AoB)o(AOC)

Answer 1



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):