Problem C. 1260. (December 2014)

C. 1260. The midpoints of sides \(\displaystyle AB\), \(\displaystyle BC\), \(\displaystyle CD\), \(\displaystyle DA\) of a unit square \(\displaystyle ABCD\) are \(\displaystyle E\), \(\displaystyle F\), \(\displaystyle I\), \(\displaystyle H\), respectively. Let \(\displaystyle M\) denote the intersection of the lines \(\displaystyle ED\) and \(\displaystyle HI\), and let \(\displaystyle G\) denote the intersection of the lines \(\displaystyle EC\) and \(\displaystyle FI\). Find the area of the quadrilateral \(\displaystyle MEGI\).

(5 pont)

Deadline expired on January 12, 2015.

Statistics:

152 students sent a solution.
5 points:	67 students.
4 points:	42 students.
3 points:	11 students.
2 points:	11 students.
1 point:	6 students.
0 point:	15 students.

Problems in Mathematics of KöMaL, December 2014