IMO Shortlist 1962 problem 3
Kvaliteta:
Avg: 3,0Težina:
Avg: 6,0 Consider the cube
(
and
are the upper and lower bases, repsectively, and edges
are parallel). The point
moves at a constant speed along the perimeter of the square
in the direction
, and the point
moves at the same rate along the perimiter of the square
in the direction
. Points
and
begin their motion at the same instant from the starting positions
and
, respectively. Determine and draw the locus of the midpionts of the segments
.
![ABCDA'B'C'D'](/media/m/2/5/6/25651bd96ec48eb07b5335ad9c983483.png)
![ABCD](/media/m/9/c/e/9ce25711ba18d9663b73c3580de4bf5a.png)
![A'B'C'D'](/media/m/e/8/1/e81445bdb3d123a9f3b5c7ffad7eed8f.png)
![AA', BB', CC', DD'](/media/m/8/5/4/8543242338fc56bb98ac1c268b7a91d3.png)
![X](/media/m/9/2/8/92802f174fc4967315c2d8002c426164.png)
![ABCD](/media/m/9/c/e/9ce25711ba18d9663b73c3580de4bf5a.png)
![ABCDA](/media/m/0/0/d/00d1eed416738a016a30d5a72bf8e44a.png)
![Y](/media/m/3/b/c/3bc24c5af9ce86a9a691643555fc3fd6.png)
![B'C'CB](/media/m/b/3/8/b38ff1d4c55bc010ef671da2b1bedce2.png)
![B'C'CBB'](/media/m/2/7/7/2778679358aebad629d382d775eb7e9a.png)
![X](/media/m/9/2/8/92802f174fc4967315c2d8002c426164.png)
![Y](/media/m/3/b/c/3bc24c5af9ce86a9a691643555fc3fd6.png)
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
![B'](/media/m/a/1/a/a1a88eb7f35fee4f41c66bfb0c902f51.png)
![XY](/media/m/1/c/e/1ce2b6bc5783d5ee7b3276a845f41d6e.png)
Izvor: Međunarodna matematička olimpijada, shortlist 1962