\(\qquad\)In a convex quadrilateral \(ABCD\) the diagonal \(BD\) does not bisect the angles \(ABC\) and \(CDA\). The point \(P\) lies inside \(ABCD\) and satisfies $$ \angle PBC = \angle DBA \;\; and \;\; \angle PDC = \angle BDA. $$ \(\qquad\)Prove that \(ABCD\) is a cyclic quadrilateral if and only if \(AP = CP\).
| Attributes | Олімпіадна |
|---|---|
| Source | International Mathematical Olympiad |
| Year | 2004 |
| Number | 5 |
| Difficulty | 10.0 |
| Themes | Геометрія |