BDMO 2016 Regional
 math_hunter
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BDMO 2016 Regional
How to solve this problem?
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 samiul_samin
 Posts: 1004
 Joined: Sat Dec 09, 2017 1:32 pm
Re: BDMO 2016 Regional
Once upon a time,I tried a lot to solve this problem but didn't find the answer.I think this is not a very tough problem.
If you connect the centers you will get a rhombus
My solution is wrong.
I am not sure about the main solution.
For posting BdMO Regional problems use the subforum named Divisional Math Olympiad.
If you connect the centers you will get a rhombus
My solution is wrong.
I am not sure about the main solution.
For posting BdMO Regional problems use the subforum named Divisional Math Olympiad.
Last edited by samiul_samin on Mon Mar 11, 2019 11:47 pm, edited 1 time in total.
 math_hunter
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 Joined: Mon Sep 24, 2018 10:33 pm
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Re: BDMO 2016 Regional
Your logic is right that if we connect the centers we'll get a rhombus. But how do you get the value of those 4 angles? And I also want to say that 42÷(tan40) is not equal to 50. So, I think that the solution isn't right.samiul_samin wrote: ↑Sun Mar 10, 2019 7:33 pmOnce upon a time,I tried a lot to solve this problem but didn't find the answer.I think this is not a very tough problem.
If you connect the centers you will get a rhombus with angles $100,100,80,80$
Than $\tan\theta=\tan {40}=\dfrac {42}{X}\Rightarrow X=50\Rightarrow 2X=\fbox {100}$(about)
Here,
$X$=radius of one big circle.
I am not sure about the main solution.
For posting BdMO Regional problems use the subforum named Divisional Math Olympiad.
 samiul_samin
 Posts: 1004
 Joined: Sat Dec 09, 2017 1:32 pm
Re: BDMO 2016 Regional
Yes,Solution is not right.
 math_hunter
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Re: BDMO 2016 Regional
How do you get those angle's value?
 samiul_samin
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Re: BDMO 2016 Regional
I used angle measuring instrument to measure them.
 math_hunter
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Re: BDMO 2016 Regional
No...no...this isn't the standard of math. You need to prove it.
 samiul_samin
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 Joined: Sat Dec 09, 2017 1:32 pm
Re: BDMO 2016 Regional
Yes.I have said that my solution is wrong.I know that.I am not eager to prove this.When I will be intersted I will try to prove.math_hunter wrote: ↑Mon Mar 11, 2019 11:40 pmNo...no...this isn't the standard of math. You need to prove it.
 math_hunter
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Re: BDMO 2016 Regional
Why are you not eager to prove this??? This is a very interesting problem.
 math_hunter
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 Joined: Mon Sep 24, 2018 10:33 pm
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Re: BDMO 2016 Regional
Ok...it's not a fact. Please try to give me the solution when you get it...