Fun math problem from IMO 2007

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In summary, the conversation discusses a problem involving a line l passing through point A and intersecting segment DC at F and line BC at G. The problem also states that the length of EF is equal to the length of EG, which is also equal to the length of EC. The goal is to prove that line l is the bisector of angle DAB in a parallelogram ABCD where BCED is a cyclic quadrilateral. There is some confusion about the wording of the problem, but it is clarified that line l intersects the line BC and not the line segment BC.
  • #1
jhooper3581
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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.
 
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  • #2
the ordering doesn't work out quite correct. is it BCED or BEDC ?
 
  • #3
It is BCED.
 
  • #4
then it is not a quadrilateral ... the diagram doesn't work out properly
 
  • #5
"intersects line BC at G."

Shouldn't that read : intersects line BC extended at G. ?
 
  • #6
uart said:
"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
rasmhop said:
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.
 

Related to Fun math problem from IMO 2007

1. What is the "Fun math problem from IMO 2007"?

The "Fun math problem from IMO 2007" refers to a question posed in the International Mathematical Olympiad (IMO) competition in the year 2007. The IMO is an annual international mathematics competition for high school students.

2. What is the International Mathematical Olympiad (IMO)?

The International Mathematical Olympiad (IMO) is an annual mathematics competition for high school students from around the world. It was first held in 1959 and has since become the most prestigious and challenging mathematics competition for high school students.

3. What is the difficulty level of the "Fun math problem from IMO 2007"?

The difficulty level of the "Fun math problem from IMO 2007" is quite high, as it was chosen as one of the six problem sets for the final round of the IMO competition. It requires advanced mathematical knowledge and problem-solving skills to solve.

4. What is the purpose of the "Fun math problem from IMO 2007"?

The main purpose of the "Fun math problem from IMO 2007" is to challenge the problem-solving abilities of high school students and to promote interest and enthusiasm for mathematics. It also serves as a platform to showcase the talents of young mathematicians from around the world.

5. Are there any resources available to help solve the "Fun math problem from IMO 2007"?

Yes, there are various resources available to help solve the "Fun math problem from IMO 2007". These include online forums, math problem-solving communities, and textbooks on advanced mathematics. It is also helpful to discuss the problem with other students or a math teacher who can provide guidance and insights.

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