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 March 10, 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 solutions.
Problems in Mathematics of KöMaL, February 2015