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Problem 2

Three sides of a trangle have the equations $L_{r}=y-m_{r} x-c_{r}=0 ; r=1,2,3\(, Then \)\lambda L_{2} L_{3}+\mu_{3} L_{1}+v L_{1} L_{2}=0$, where \(\lambda \neq 0, \mu \neq 0, v \neq 0\), is the equation of circumcircle of triangle, if : : (a) \(\lambda\left(m_{2}+m_{3}\right)+\mu\left(m_{3}+m_{1}\right)+v\left(m_{1}+m_{2}\right)=0\) (b) $\lambda\left(m_{2} m_{3}-1\right)+\mu\left(m_{3} m_{1}-1\right)+v\left(m_{1} m_{2}-1\right)=0$ (c) both (a) and (b) (d) none of these

Expert verified

The detailed solution could vary based on the specifics of the \(m_r\) and \(c_r\) values given, which are not provided in the problem. However, based on the procedure outlined above, it's possible to determine which of the options (a), (b), (c), or (d) is correct.

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