A) right angled
B) equilateral
C) isosceles
D) None of these
Correct Answer: D
Solution :
[d] \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}={{c}^{2}}(a+b+c)\] \[\Rightarrow \,\,\,\,\,\,\,{{a}^{3}}+{{b}^{3}}=a{{c}^{2}}+b{{c}^{2}}\] \[\Rightarrow \,\,\,\,\,\,\,{{a}^{3}}+{{b}^{3}}=a{{c}^{2}}+b{{c}^{2}}\] \[\Rightarrow \,\,\,\,\,\,\,a({{a}^{2}}-{{c}^{2}})=b\,({{c}^{2}}-{{b}^{2}})\] \[\Rightarrow \,\,\,\,\,\,\,\sin A\,\,\sin (A-C)\,\,\sin (A+C)\] \[=\sin B\sin (C-B).\sin (C+B)\] \[\Rightarrow \,\,\,A-C=C-B\] \[\Rightarrow \,\,\,A+B=2C\] \[\Rightarrow \,\,\,C=60{}^\circ \]
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