Fun math problem from IMO 2007

  • #1
2. Consider five points A, B, C, D and E such that ABCD is a parallelogram and BCED is a cyclic quadrilateral. Let [itex]l[/itex] be a line passing through A. Suppose that [itex]l[/itex] intersects the interior of the segment DC at F and intersects line BC at G. Suppose also that EF = EG = EC. Prove that [itex]l[/itex] is the bisector of angle DAB.
 

Answers and Replies

  • #2
35
0
the ordering doesn't work out quite correct. is it BCED or BEDC ?
 
  • #3
It is BCED.
 
  • #4
35
0
then it is not a quadrilateral ... the diagram doesnt work out properly
 
  • #5
uart
Science Advisor
2,797
21
"intersects line BC at G."

Shouldn't that read : intersects line BC extended at G. ?
 
  • #6
430
3
"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.
 
  • #7
uart
Science Advisor
2,797
21
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.
 
  • #8
nirax, my problem wordings are correct. Please look again and think about it a little bit more.
 

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