Fun math problem from IMO 2007

  • Context: Graduate 
  • Thread starter Thread starter jhooper3581
  • Start date Start date
  • Tags Tags
    Fun
Click For Summary

Discussion Overview

The discussion revolves around a mathematical problem from the International Mathematical Olympiad (IMO) 2007, specifically involving a configuration of points and lines related to a parallelogram and a cyclic quadrilateral. Participants are analyzing the conditions and implications of the problem statement.

Discussion Character

  • Technical explanation, Debate/contested

Main Points Raised

  • One participant presents a problem involving points A, B, C, D, and E, asserting that line l intersects segment DC at F and line BC at G, with the condition that EF = EG = EC.
  • Another participant questions the ordering of points in the cyclic quadrilateral, suggesting it may be incorrectly labeled as BCED.
  • A subsequent reply confirms the ordering as BCED, but raises concerns about the diagram's accuracy.
  • There is a discussion about the phrasing of the intersection of line l with line BC, with one participant suggesting it should specify "line BC extended," while another defends the original wording as correct.
  • Clarifications are made regarding the nature of line BC, with emphasis on it being an infinitely long line rather than a segment.
  • One participant insists that their original wording is accurate and encourages others to reconsider their understanding of the problem.

Areas of Agreement / Disagreement

Participants express disagreement regarding the interpretation of the problem's wording and the configuration of points. There is no consensus reached on these points, and the discussion remains unresolved.

Contextual Notes

There are potential limitations in the clarity of the problem statement and the assumptions regarding the configuration of points and lines, which may affect participants' interpretations.

jhooper3581
Messages
49
Reaction score
0
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.
 
Mathematics news on Phys.org
the ordering doesn't work out quite correct. is it BCED or BEDC ?
 
It is BCED.
 
then it is not a quadrilateral ... the diagram doesn't work out properly
 
"intersects line BC at G."

Shouldn't that read : intersects line BC extended at G. ?
 
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.
 
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.
 
nirax, my problem wordings are correct. Please look again and think about it a little bit more.
 

Similar threads

Graduate Prove: Angle DAB Bisector when Given Parallelogram ABCD, Cyc. Quadrilateral BCED
  • · Replies 1 ·
Replies
1
Views
2K
Challenge Ready for a Summer Math Challenge?
  • · Replies 62 ·
3
Replies
62
Views
12K
Graduate What Does Mathematical Sameness Mean?
  • · Replies 7 ·
Replies
7
Views
3K
Mathematica This Week's Finds in Mathematical Physics (Week 266)
  • · Replies 1 ·
Replies
1
Views
4K
Mathematica This Week's Finds in Mathematical Physics (Week 236)
  • · Replies 7 ·
Replies
7
Views
4K
Mathematica This Week's Finds in Mathematical Physics (Week 236)
  • · Replies 9 ·
Replies
9
Views
4K