খাইছে আইএমওতেও কমন পড়ে!!!

[Tahmid Hasan]

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 ]

[*Mahi*]

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.

[Tahmid Hasan]

Mahi,could you please specify the problem?

[*Mahi*]

IMO 1999 G8 ( http://www.matholympiad.org.bd/forum/vi ... =17&t=2053 )