Geometry Problem 1249

Elements: Cyclic Quadrilateral, Circle, Triangle, Circumcircle, Angle Bisector, Parallel Lines, Area

A quadrilateral ABCD is inscribed in a circle O as shown in the figure below. F is on CB extended so that AC is the bisector of angle FAD and FA is parallel to BD. AC and BD cut at E. The circle of center O and radius OE cuts AC at Y. The circumcircle O1 of the triangle EDY cuts AD at X. Prove that the areas of the triangles AEX and AEB are equal.
This entry contributed by Sumith Peiris, Moratuwa, Sri Lanka.


Geometry Problem 1249: Cyclic Quadrilateral, Circle, Triangle, Circumcircle, Angle Bisector, Parallel Lines, Area