KöMaL - Középiskolai Matematikai és Fizikai Lapok
Sign In
Sign Up
 Magyar
Information
Contest
Journal
Articles

 

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.

Our web pages are supported by:   Ericsson   Cognex   Emberi Erőforrás Támogatáskezelő   Emberi Erőforrások Minisztériuma   Nemzeti Tehetség Program    
MTA Energiatudományi Kutatóközpont   MTA Wigner Fizikai Kutatóközpont     Nemzeti
Kulturális Alap   ELTE   Morgan Stanley