South Africa national 1999-3-The bisector of $\angle{BAD}$ in the parallellogram $ABCD$ intersects the lines $BC$ and $CD$ at the points $K$ and $L$ respectively. Prove that the centre of the circle passing through the points $C,K,L$ lies on the circle passing through the points $B,C,D$.
IMO-2007-2-Consider five points $A,B,C,D,E$ such that $ABCD$ is a parallelogram and $BCED$ is a cyclic quadrilateral.Let $\ell$ be a line passing through $A$.Suppose that $\ell$ intersects the interior of the segment $DC$ at $F$ and intersects line $BC$ at $G$.Suppose also that $EF = EG = EC$.Prove that $\ell$ is the bisector of $\angle {DAB}$.
[এইডা ক্যামনে সম্ভব,শুধু দুইটা condition উল্টায় দিলে ত প্রবলেম পুরাই মিলে যায় ]
খাইছে আইএমওতেও কমন পড়ে!!!
- Tahmid Hasan
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Re: খাইছে আইএমওতেও কমন পড়ে!!!
Iran 1998 (TST maybe) had a problem which appeared in IMO next year (That exact problem.) That happened because that problem had an general idea. I think this is the case with this one too.
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Nur Muhammad Shafiullah | Mahi
Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi
- Tahmid Hasan
- Posts:665
- Joined:Thu Dec 09, 2010 5:34 pm
- Location:Khulna,Bangladesh.
Re: খাইছে আইএমওতেও কমন পড়ে!!!
IMO 1999 G8 ( http://www.matholympiad.org.bd/forum/vi ... =17&t=2053 )
Please read Forum Guide and Rules before you post.
Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi
Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi