Problem C. 1276. (February 2015)
C. 1276. \(\displaystyle X\), \(\displaystyle Y\), \(\displaystyle Z\), \(\displaystyle V\) are interior points of sides \(\displaystyle AB\), \(\displaystyle BC\), \(\displaystyle CD\), \(\displaystyle DA\) of a parallelogram \(\displaystyle ABCD\), respectively, such that \(\displaystyle \frac{AX}{XB} =\frac{BY}{YC}
=\frac{CZ}{ZD} =\frac{DV}{VA}=k\), where \(\displaystyle k\) is a positive constant less than \(\displaystyle \frac
12\). Find the value of \(\displaystyle k\), given that the area of quadrilateral \(\displaystyle XYZV\) is 68% of the area of parallelogram \(\displaystyle ABCD\).
(5 pont)
Deadline expired on 10 March 2015.
Statistics:
115 students sent a solution.  
5 points:  65 students. 
4 points:  20 students. 
3 points:  14 students. 
2 points:  6 students. 
1 point:  5 students. 
0 point:  4 students. 
Unfair, not evaluated:  1 solution. 
