jee-main 2023 Q69

jee-main · India · session1_01feb_shift1 Sine and Cosine Rules Multi-step composite figure problem

For a triangle $ABC$, the value of $\cos 2A + \cos 2B + \cos 2C$ is least. If its inradius is 3 and incentre is $M$, then which of the following is NOT correct?
(1) Perimeter of $\triangle ABC$ is $18\sqrt{3}$
(2) $\sin 2A + \sin 2B + \sin 2C = \sin A + \sin B + \sin C$
(3) $\overrightarrow{MA} \cdot \overrightarrow{MB} = -18$
(4) area of $\triangle ABC$ is $\frac{27\sqrt{3}}{2}$

For a triangle $ABC$, the value of $\cos 2A + \cos 2B + \cos 2C$ is least. If its inradius is 3 and incentre is $M$, then which of the following is NOT correct?\\
(1) Perimeter of $\triangle ABC$ is $18\sqrt{3}$\\
(2) $\sin 2A + \sin 2B + \sin 2C = \sin A + \sin B + \sin C$\\
(3) $\overrightarrow{MA} \cdot \overrightarrow{MB} = -18$\\
(4) area of $\triangle ABC$ is $\frac{27\sqrt{3}}{2}$

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