IMO Shortlist 2002 problem G8
Kvaliteta:
Avg: 4,0Težina:
Avg: 9,0 Let two circles
and
meet at the points
and
. A line through
meets
again at
and
again at
. Let
,
,
be three points on the line segments
,
,
respectively, with
parallel to
and
parallel to
. Let
and
be points on those arcs
of
and
of
respectively that do not contain
. Given that
is perpendicular to
and
is perpendicular to
prove that
.
![S_{1}](/media/m/c/3/2/c32b2ccf37ad57aa0ac979e8922c268a.png)
![S_{2}](/media/m/a/9/4/a94de2299932dfc5d3bb6afed0ea0bf3.png)
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
![B](/media/m/c/e/e/ceebc05be717fa6aab8e71b02fe3e4e3.png)
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
![S_{1}](/media/m/c/3/2/c32b2ccf37ad57aa0ac979e8922c268a.png)
![C](/media/m/5/a/b/5ab88f3f735b691e133767fe7ea0483c.png)
![S_{2}](/media/m/a/9/4/a94de2299932dfc5d3bb6afed0ea0bf3.png)
![D](/media/m/7/0/0/7006c4b57335ab717f8f20960577a9ef.png)
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
![N](/media/m/f/1/9/f19700f291b1f2255b011c11d686a4cd.png)
![K](/media/m/e/1/e/e1ed1943d69f4d6a840e99c7bd199930.png)
![CD](/media/m/8/9/5/895081147290365ccae028796608097d.png)
![BC](/media/m/5/0/0/5005d4d5eac1b420fbabb76c83fc63ad.png)
![BD](/media/m/1/1/f/11f65a804e5c922ee28a53b1df04d138.png)
![MN](/media/m/2/6/7/267a73297a5de9e529d41774ee6ff45a.png)
![BD](/media/m/1/1/f/11f65a804e5c922ee28a53b1df04d138.png)
![MK](/media/m/5/b/e/5bec85a3fcbcd7885b11b39231145af0.png)
![BC](/media/m/5/0/0/5005d4d5eac1b420fbabb76c83fc63ad.png)
![E](/media/m/8/b/0/8b01e755d2253cb9a52f9e451d89ec11.png)
![F](/media/m/3/e/8/3e8bad5df716d332365fca76f53c1743.png)
![BC](/media/m/5/0/0/5005d4d5eac1b420fbabb76c83fc63ad.png)
![S_{1}](/media/m/c/3/2/c32b2ccf37ad57aa0ac979e8922c268a.png)
![BD](/media/m/1/1/f/11f65a804e5c922ee28a53b1df04d138.png)
![S_{2}](/media/m/a/9/4/a94de2299932dfc5d3bb6afed0ea0bf3.png)
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
![EN](/media/m/8/a/7/8a738873fd9bb9b92a40601aa803337f.png)
![BC](/media/m/5/0/0/5005d4d5eac1b420fbabb76c83fc63ad.png)
![FK](/media/m/1/8/5/185a554a2095520f3032542c84f6aa69.png)
![BD](/media/m/1/1/f/11f65a804e5c922ee28a53b1df04d138.png)
![\angle EMF=90^{\circ}](/media/m/f/f/0/ff0920ba292e7bd9765ea24e3dfe5abe.png)
Izvor: Međunarodna matematička olimpijada, shortlist 2002