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.
BdMO National Secondary 2011/5
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin
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- FahimFerdous
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Re: BdMO National Secondary 2011/5
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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Re: BdMO National Secondary 2011/5
Solved here.FahimFerdous wrote: ↑Sun Feb 13, 2011 9:25 pmIt'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.