BdMO '16 regional junior/9

For students of class 6-8 (age 12 to 14)
Absur Khan Siam
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Location:Bashaboo , Dhaka
BdMO '16 regional junior/9

Unread post by Absur Khan Siam » Fri Dec 30, 2016 11:33 am

Need help to solve this problem.
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"(To Ptolemy I) There is no 'royal road' to geometry." - Euclid

SMMamun
Posts:57
Joined:Thu Jan 20, 2011 6:57 pm

Re: BdMO '16 regional junior/9

Unread post by SMMamun » Sat Dec 31, 2016 4:46 am

There are many symmetrical parts in the picture. You can establish relationship among the radii and several other line segments by applying symmetry. If you consider the radius of the smaller circle(s) "x" and the radius of the larger circle(s) "y", can you develop an equation between them? And then why don't you connect the centers and a point of tangent to see whether a right triangle can be formed in order to apply the Pythagorean theorem involving x & y? :)

* By the way, description/language of the problem should have been a little more elaborate and clarified.

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Thanic Nur Samin
Posts:176
Joined:Sun Dec 01, 2013 11:02 am

Re: BdMO '16 regional junior/9

Unread post by Thanic Nur Samin » Sat Dec 31, 2016 12:52 pm

A different point of view, one can also use Descartes' theorem.

https://en.wikipedia.org/wiki/Descartes'_theorem
Hammer with tact.

Because destroying everything mindlessly isn't cool enough.

Zahin Hasin Rudro
Posts:11
Joined:Sun Jul 12, 2015 3:52 am

Re: BdMO '16 regional junior/9

Unread post by Zahin Hasin Rudro » Wed Jan 04, 2017 6:15 pm

Hint:construct an isosceles triangle by joining the center of any small circle with the two big circles, then form an equation,solve it.......

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