## BdMO 2017 National Round Secondary 9

- Kazi_Zareer
**Posts:**86**Joined:**Thu Aug 20, 2015 7:11 pm**Location:**Malibagh,Dhaka-1217

### BdMO 2017 National Round Secondary 9

In a cyclic quadrilateral $ABCD$ with circumcenter $O,$ the lines $BC$ and $AD$ intersect at $E.$ The lines $AB$ and $CD$ intersect at $F.$ A point $P$ satisfying $\angle EPD = \angle FPD = \angle BAD$ is chosen inside of $ABCD.$ The line $FO$ intersects the lines $AD,EP,BC$ at $X,Q,Y$ respectively. Also $\angle DQX = \angle CQY.$ What is the $\angle AEB$?

We cannot solve our problems with the same thinking we used when we create them.

### Re: BdMO 2017 National Round Secondary 9

**The first principle is that you must not fool yourself and you are the easiest person to fool.**

### Re: BdMO 2017 National Round Secondary 9

How to draw a good diagram for this? I couldnt construct the point P with hands..tried for a long time..