Difference between revisions of "2004 IMO Problems/Problem 5"
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==Solution== | ==Solution== | ||
{{solution}} | {{solution}} | ||
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| + | 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>, | ||
==See Also== | ==See Also== | ||
{{IMO box|year=2004|num-b=4|num-a=6}} | {{IMO box|year=2004|num-b=4|num-a=6}} | ||
Revision as of 15:30, 8 February 2024
Problem
In a convex quadrilateral 
, the diagonal 
bisects neither the angle 
nor the angle 
. The point 
lies inside and satisfies ![\[\angle PBC = \angle DBA \text{ and } \angle PDC = \angle BDA.\]](http://latex.artofproblemsolving.com/9/7/7/977f696cf8654292a2d57df388ce9a1baff926af.png)
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.
Let 
be the intersection of 
and 
, let 
be the intersection of and 
,
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 | ||
