2004 IMO Problems/Problem 5
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
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 .
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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 |