china fun( do it to learn something)

For discussing Olympiad level Geometry Problems
ishfaqhaque
Posts:20
Joined:Thu Dec 09, 2010 3:30 pm
china fun( do it to learn something)

Unread post by ishfaqhaque » Wed Jan 05, 2011 7:55 pm

To all,
to solve this you might need something that plays a vital role in so many problems. so please try this and learn that thing

Given an acute triangle $PBC $with $PB\neq PC$. Points$ A,D $lie on $PB,PC, $respectively. $AC$ intersects $BD$ at point $O$. Let $E,F $be the feet of perpendiculars from $O$ to$ AB,CD$, respectively. Denote by $M,N $the midpoints of $BC,AD.$
(1): If four points $A,B,C,D$ lie on one circle, then$ EM\cdot FN = EN\cdot FM.$
(2): Determine whether the converse of (1) is true or not, justify your answer.

Post Reply