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.

### 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.

Problems in Mathematics of KöMaL, February 2015