Fun math problem from IMO 2007

[jhooper3581]

2. Consider five points A, B, C, D and E such that ABCD is a parallelogram and BCED is a cyclic quadrilateral. Let $l$ be a line passing through A. Suppose that $l$ intersects the interior of the segment DC at F and intersects line BC at G. Suppose also that EF = EG = EC. Prove that $l$ is the bisector of angle DAB.

 

[nirax]

the ordering doesn't work out quite correct. is it BCED or BEDC ?

 

[jhooper3581]

It is BCED.

 

[nirax]

then it is not a quadrilateral ... the diagram doesn't work out properly

 

[uart]

"intersects line BC at G."

Shouldn't that read : intersects line BC extended at G. ?

 

[rasmhop]

"intersects line BC at G."

Shouldn't that read : intersects line BC extended at G. ?

No the original wording is correct. He said line (infinitely long), not line segment. It doesn't really make sense to speak of extending a line.

 

[uart]

No the original wording is correct. He said line (infinitely long), not line segment. It doesn't really make sense to speak of extending a line.

Ok so it doesn't intersect the line segment BC, that's all the clarification I was looking for.

 

[jhooper3581]

nirax, my problem wordings are correct. Please look again and think about it a little bit more.