IGO 2016 Elementary/4

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IGO 2016 Elementary/4

Post Number:#1  Unread postby Thamim Zahin » Tue Jan 10, 2017 2:19 pm

4. In a right-angled triangle $ABC (\angle A = 90)$, the perpendicular bisector of $BC$ intersects the line $AC$ in $K$ and the perpendicular bisector of $BK$ intersects the line $AB$ in $L$. If the line $CL$ be the internal bisector of $\angle C$, find all possible values for angles $\angle B$ and $\angle C$.
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Re: IGO 2016 Elementary/4

Post Number:#2  Unread postby aritra barua » Sat Feb 25, 2017 12:33 pm

Isn't BC the diameter of the circumcircle?
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Re: IGO 2016 Elementary/4

Post Number:#3  Unread postby ahmedittihad » Sat Feb 25, 2017 4:50 pm

Yes. It's a very trivial observation. Try to solve the problem.
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Re: IGO 2016 Elementary/4

Post Number:#4  Unread postby Thamim Zahin » Sun Feb 26, 2017 12:04 am

The fun thing(or cruel) about this problem is: You don't even have to do angle chasing in this problem. But when it is saying something about $90^o$, all we want is diameter. Through, use everything you learnt in class $6,7,8$. By that, you might solve the problem.
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Re: IGO 2016 Elementary/4

Post Number:#5  Unread postby ahmedittihad » Sun Feb 26, 2017 8:24 am

Why couldn't you? Thamim
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