Difference between revisions of "2004 IMO Problems/Problem 5"
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− | + | Assume <math>ABCD</math> is cyclic, | |
+ | let <math>K</math> be the intersection of <math>AC</math> and <math>BE</math>, let <math>L</math> be the intersection of <math>AC</math> and <math>DF</math>, | ||
<asy> | <asy> |
Revision as of 21:28, 8 February 2024
Problem
In a convex quadrilateral , the diagonal bisects neither the angle nor the angle . The point lies inside and satisfies
Prove that is a cyclic quadrilateral if and only if
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
Assume is cyclic, let be the intersection of and , let be the intersection of and ,
, so , and . , so , and .
, so is an isosceles triangle. Since , so and are isosceles triangles. So is on the perpendicular bisector of , since is an isosceles trapezoid, so is also on the perpendicular bisector of . So .
~szhangmath
See Also
2004 IMO (Problems) • Resources | ||
Preceded by Problem 4 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 6 |
All IMO Problems and Solutions |