BdMO '16 regional junior/9
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- Location:Bashaboo , Dhaka
Need help to solve this problem.
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"(To Ptolemy I) There is no 'royal road' to geometry." - Euclid
Re: BdMO '16 regional junior/9
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.
* By the way, description/language of the problem should have been a little more elaborate and clarified.
- Thanic Nur Samin
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- Joined:Sun Dec 01, 2013 11:02 am
Re: BdMO '16 regional junior/9
A different point of view, one can also use Descartes' theorem.
https://en.wikipedia.org/wiki/Descartes'_theorem
https://en.wikipedia.org/wiki/Descartes'_theorem
Hammer with tact.
Because destroying everything mindlessly isn't cool enough.
Because destroying everything mindlessly isn't cool enough.
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Re: BdMO '16 regional junior/9
Hint:construct an isosceles triangle by joining the center of any small circle with the two big circles, then form an equation,solve it.......