Who Wants to Solve an IMO Problem?
by djmathman, Jun 10, 2013, 12:54 AM
I do I do I do
EDIT: Ooh I realized this was an IMO problem and not just an ISL problem cool
EDIT: Ooh I realized this was an IMO problem and not just an ISL problem cool
IMO 2000.1 wrote:
Two circles 
and 
intersect at two points 
and 
. Let 
be the line tangent to these circles at 
and 
, respectively, so that lies closer to than . Let 
be the line parallel to and passing through the point , with 
on and 
on . Lines 
and 
meet at 
; lines 
and meet at 
; lines 
and meet at 
. Show that 
.
and 
intersect at two points 
and 
. Let 
be the line tangent to these circles at 
and 
, respectively, so that lies closer to than . Let 
be the line parallel to and passing through the point , with 
on and 
on . Lines 
and 
meet at 
; lines 
and meet at 
; lines 
and meet at 
. Show that 
.
.
lies on the radical axis of 
and 
,
,
to 
gives 
.
we have 
,
.
,
and 
so that 
are collinear in that order. Note that![\[\angle EAB=\angle ECD=\angle CAE=\angle CMA=\angle MAB,\]](http://latex.artofproblemsolving.com/d/4/3/d43644db7cba14afe7d6037fd8b216a529a0f9d3.png)
step was taken because the measures of both angles are equal to 
.
,
.
is a kite, so 
,
This post has been edited 4 times. Last edited by djmathman, Sep 5, 2013, 1:30 AM
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