Mathematical and Physical Journal
for High Schools
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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.


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.

Problems in Mathematics of KöMaL, February 2015