Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
Already signed up?
New to KöMaL?

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