\((1)\) 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.

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TopNewestFor problem 1 apply titus lemma in the constraint given and then apply AM GM and it's done. – Racchit Jain · 2 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 · 2 weeks ago

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check this one – Shivam Jadhav · 1 week, 6 days ago

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