IMO Shortlist 1995 problem G1
Kvaliteta:
Avg: 0,0Težina:
Avg: 6,0 Let
be four distinct points on a line, in that order. The circles with diameters
and
intersect at
and
. The line
meets
at
. Let
be a point on the line
other than
. The line
intersects the circle with diameter
at
and
, and the line
intersects the circle with diameter
at
and
. Prove that the lines
are concurrent.
![A,B,C,D](/media/m/8/5/d/85d135de173dbb765c7a2f175c5b2f60.png)
![AC](/media/m/6/4/7/647ef3a5d68f07d59d84afe03a9dc655.png)
![BD](/media/m/1/1/f/11f65a804e5c922ee28a53b1df04d138.png)
![X](/media/m/9/2/8/92802f174fc4967315c2d8002c426164.png)
![Y](/media/m/3/b/c/3bc24c5af9ce86a9a691643555fc3fd6.png)
![XY](/media/m/1/c/e/1ce2b6bc5783d5ee7b3276a845f41d6e.png)
![BC](/media/m/5/0/0/5005d4d5eac1b420fbabb76c83fc63ad.png)
![Z](/media/m/7/9/4/794ff2bd637e30ea27e50e57eecd0b76.png)
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
![XY](/media/m/1/c/e/1ce2b6bc5783d5ee7b3276a845f41d6e.png)
![Z](/media/m/7/9/4/794ff2bd637e30ea27e50e57eecd0b76.png)
![CP](/media/m/6/3/0/630424587cadeb75669118dab3df6b98.png)
![AC](/media/m/6/4/7/647ef3a5d68f07d59d84afe03a9dc655.png)
![C](/media/m/5/a/b/5ab88f3f735b691e133767fe7ea0483c.png)
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
![BP](/media/m/e/e/f/eefb4fe46ab8d85b7067c29b24aa4cfc.png)
![BD](/media/m/1/1/f/11f65a804e5c922ee28a53b1df04d138.png)
![B](/media/m/c/e/e/ceebc05be717fa6aab8e71b02fe3e4e3.png)
![N](/media/m/f/1/9/f19700f291b1f2255b011c11d686a4cd.png)
![AM,DN,XY](/media/m/3/6/2/3628ecadd4d8a8bf2ac80a4c661a4382.png)
Izvor: Međunarodna matematička olimpijada, shortlist 1995