Difference between revisions of "1960 IMO Problems/Problem 5"

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Consider the cube <math>ABCDA'B'C'D'</math> (with face <math>ABCD</math> directly above face <math>A'B'C'D'</math>).  
 
Consider the cube <math>ABCDA'B'C'D'</math> (with face <math>ABCD</math> directly above face <math>A'B'C'D'</math>).  
  
a) Find the locus of the midpoints of the segments <math>XY</math>, where <math>X</math> is any point of <math>AC</math> and <math>Y</math> is any piont of <math>B'D'</math>;
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a) Find the locus of the midpoints of the segments <math>XY</math>, where <math>X</math> is any point of <math>AC</math> and <math>Y</math> is any point of <math>B'D'</math>;
  
 
b) Find the locus of points <math>Z</math> which lie on the segment <math>XY</math> of part a) with <math>ZY = 2XZ</math>.
 
b) Find the locus of points <math>Z</math> which lie on the segment <math>XY</math> of part a) with <math>ZY = 2XZ</math>.

Revision as of 13:58, 28 October 2007

Problem

Consider the cube $ABCDA'B'C'D'$ (with face $ABCD$ directly above face $A'B'C'D'$).

a) Find the locus of the midpoints of the segments $XY$, where $X$ is any point of $AC$ and $Y$ is any point of $B'D'$;

b) Find the locus of points $Z$ which lie on the segment $XY$ of part a) with $ZY = 2XZ$.

Solution

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See Also

1960 IMO (Problems) • Resources
Preceded by
Problem 4
1 2 3 4 5 6 Followed by
Problem 6
All IMO Problems and Solutions
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