in a triangle ABC, (a+b+c)(b+c-a)=Λbc if......(condition)?

Dear nishant

(a+b+c)(b+c-a)=abc

((b+c)+a)((b+c)-a)=abc

 (b+c)² -a² =abc

 b² +c² +2bc -a² =abc

b² +c²  -a² =abc -2bc

(b² +c²  -a²)/2bc =a/2 - 1

 cosA =a/2 - 1

 since  -1< cosA <1

  so          -1< a/2 - 1 <1

                0< a/2<2

                0<a<4

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