IMO Shortlist 2001 problem G1
Kvaliteta:
Avg: 0,0Težina:
Avg: 6,0 Let
be the center of the square inscribed in acute triangle
with two vertices of the square on side
. Thus one of the two remaining vertices of the square is on side
and the other is on
. Points
are defined in a similar way for inscribed squares with two vertices on sides
and
, respectively. Prove that lines
are concurrent.
![A_1](/media/m/5/a/6/5a6ce1347567551c02239ff8d4ebee67.png)
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
![BC](/media/m/5/0/0/5005d4d5eac1b420fbabb76c83fc63ad.png)
![AB](/media/m/5/2/9/5298bd9e7bc202ac21c423e51da3758e.png)
![AC](/media/m/6/4/7/647ef3a5d68f07d59d84afe03a9dc655.png)
![B_1,\ C_1](/media/m/c/7/7/c77861ea0e16fcea11ec821c7b2eb666.png)
![AC](/media/m/6/4/7/647ef3a5d68f07d59d84afe03a9dc655.png)
![AB](/media/m/5/2/9/5298bd9e7bc202ac21c423e51da3758e.png)
![AA_1,\ BB_1,\ CC_1](/media/m/5/5/6/556f737104137ecf070af64ec696423a.png)
Izvor: Međunarodna matematička olimpijada, shortlist 2001