O is any point in the interior of triangle ABC bisector of angleaob,angle boc and angle aoc intersect side ab, side bc ,side ac in f d e prove that bf x ae x cd =af x ce x bd
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HEY MATE
BELOW IS YOUR ANSWER ✌✌
IN ABC
< AOB , < BOC AND < AOC INTERSECT BC , AC , AB IN F ,D, E
IN AOB
OF IS BISECTOR
AF / BF = OA / OB ..( BY ANGLE BISECTOR THEOREM )
AF x OB = BF x OA ..)(1#1
IN AOC
OE IS BISECTOR
BY ANGLE BISECOR THEOREM
AE / CE = OA/ OC
AE x OC = CE X OA
OA X CE = AE X OC .. (2)
IN BOC
OD IS BISECTOR
BY ANGLE BISECTOR THEOREM
BD / DC = OB/ DC
BD X OC = OB X DC ..(3)
FROM 1,2 ,3
=AF X OB X OA X CE XBD X OC = BF X OA X AE X OC X OB X DC
= AF X CE X BD = BF X AE X CD
= BF X AE X CD= AF X CE X BD
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