BdMO National Secondary 2011/5

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Moon
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BdMO National Secondary 2011/5

Unread post by Moon » Fri Feb 11, 2011 1:49 pm

Problem 5:
In a scalene triangle $ABC$ with $\angle A = 90^{\circ}$, the tangent line at $A$ to its circumcircle meets line $BC$ at $M$ and the incircle touches $AC$ at $S$ and $AB$ at $R$. The lines $RS$ and $BC$ intersect at $N$ while the lines $AM$ and $SR$ intersect at $U$. Prove that the triangle $UMN$ is isosceles.
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FahimFerdous
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Re: BdMO National Secondary 2011/5

Unread post by FahimFerdous » Sun Feb 13, 2011 9:25 pm

It's the same as h.secondary problem 5. I've posted the solution in that topic. As I'm using mobile, I can't copy-paste it. So, if anyone wants, he/she can get it from H.Secondary problem no 5. :-)
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samiul_samin
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Re: BdMO National Secondary 2011/5

Unread post by samiul_samin » Mon Feb 25, 2019 3:44 pm

FahimFerdous wrote:
Sun Feb 13, 2011 9:25 pm
It's the same as h.secondary problem 5. I've posted the solution in that topic. As I'm using mobile, I can't copy-paste it. So, if anyone wants, he/she can get it from H.Secondary problem no 5. :-)
Solved here.

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