## BdMO 2017 National Round Secondary 9

Discussion on Bangladesh Mathematical Olympiad (BdMO) National
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.

joydip
Posts: 49
Joined: Tue May 17, 2016 11:52 am

### 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.

NOBODY
Posts: 2
Joined: Sat Feb 04, 2017 8:34 pm

### 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..