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

@Racchit Jain

Is RMO DELHI results out?

At which website? · 2 months, 3 weeks ago

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

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

@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. · 3 months, 1 week ago