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INMO 2017 Board

\((1)\) Let \({ x }_{ 1 },...,{ x }_{ 2017 }\) be positive reals such that

\(\huge\ \frac { 1 }{ { x }_{ 1 }+2017 } +\frac { 1 }{ { x }_{ 2 }+2017 } +...+\frac { 1 }{ { x }_{ 2017
}+2017 } =\frac { 1 }{ 2017 }\)

Prove that

\(\huge\ \frac { \sqrt [ 2017 ]{ { x }_{ 1 }{ x }_{ 2 }...{ x }_{ 2017 } } }{ 2016 } \ge 2017\)


Two circles enclose non-intersecting areas. Common tangent lines to the two circles, one external and one internal, are drawn. Consider two straight lines each of which passes through the tangent points on one of the circles. Prove that the intersection point of the lines lies on the straight line that connects the centers of the circles.


Hello everybody. Please post solutions of these problems and post problems on your own also.

These are sample problems.

Note by Priyanshu Mishra
3 months, 1 week ago

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INMO 2017 Solution- www.zeal.academy http://www.zeal.academy/INMO%202017%20solutions(HM).pdf Zeal Academy · 3 days, 4 hours ago

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Where are the new problems. Aaron Jerry Ninan · 2 weeks, 6 days ago

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@Sharky Kesa,

Try the new problems Priyanshu Mishra · 2 months, 1 week ago

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@Sharky Kesa, @Harsh Shrivastava,

i HAve added newproblems. TRy them. Priyanshu Mishra · 2 months, 1 week ago

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Any more problems? Sharky Kesa · 2 months, 3 weeks ago

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For problem 1 apply titus lemma in the constraint given and then apply AM GM and it's done. Racchit Jain · 3 months, 1 week ago

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@Racchit Jain @Racchit Jain

Is RMO DELHI results out?

At which website? Priyanshu Mishra · 2 months, 3 weeks ago

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@Priyanshu Mishra They send you your marks by mail. Only marks though, the cutoff hasn't been decided yet. Racchit Jain · 2 months, 3 weeks ago

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@Racchit Jain At which website is the name of list of selected students declared? Priyanshu Mishra · 2 months, 3 weeks ago

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@Priyanshu Mishra It's not declared yet but I think it will be on hbcse Racchit Jain · 2 months, 3 weeks ago

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@Harsh Shrivastava, @Sharky Kesa, @Svatejas Shivakumar, @rajdeep das, @Racchit Jain,@Vaibhav Prasad @Kalash Verma @Nihar Mahajan @Adarsh Kumar @Akshat Sharda @AkshayYadav @Swapnil Das @Rajdeep Dhingra @Anik Mandal @Lakshya Sinha @Abhay Kumar @Dev Sharma and everyone.

Come and enjoy solving problems here. Priyanshu Mishra · 3 months, 1 week ago

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check this one Shivam Jadhav · 3 months, 1 week ago

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