# a + b + c

In the triangle ABC , If ( a + b + c )(a + b - c) = k ab

Prove that : k $$\in \left( 0,2 \right) \quad ,\quad then\quad find\quad m\quad \left( \angle c \right) \quad when\quad k=1\quad$$

Note by Rawan Medhat
2 years, 8 months ago

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If ( a + b + c )(a + b - c) = kab then a²+b² -c²=(k-2)ab and thus cos(C)=(a²+b² -c²)/(2ab) =(k-2)/2 and -1≤cos(C)≤0 or -1≤(k-2)/2≤0 or 0≤(k≤2. Further if k=1 then cos(C)=(k-2)/2= (1-2)/2=-1/2 or C=120°.

- 2 years, 8 months ago