Oktay Mercimek, EMAT 6690

Bisectors Problem in 120 degree Obtuse Triangle

Theorem 2:

If AA' =Z is angle bisector then

Lemma:      (When Z is the Angle bisector.)

            proof of lemma:  

                           QED.

Proof of Theorem2:

Using Cosine Theorem

  then ,

so

 therefore,                                          (*1)

  Using cosine theorem for Triangle ABA' ;                                  (*2)

   Using cosine theorem for Triangle AA'C;                                     (*3)

Adding (*1) , (*2) and (*3) gives :

                                             (*4)

Now we can use Lemma to simplify this identity.

Lemma is        then multiplying both sides with ;

       so       (*5)

Adding (*4) and (*5) gives

then          and

                   QED

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