Problem C. 1317. (November 2015)

C. 1317. The interior angles lying at vertices \(\displaystyle A\), \(\displaystyle B\), \(\displaystyle C\) and \(\displaystyle D\) of a pentagon \(\displaystyle ABCDE\) are \(\displaystyle 90^\circ\), \(\displaystyle 60^\circ\), \(\displaystyle 150^\circ\) and \(\displaystyle 150^\circ\), respectively. Furthermore \(\displaystyle AB=2BC=\frac 43 AD\). Prove that the line segment joining the intersection of lines \(\displaystyle AE\) and \(\displaystyle CD\) to the intersection of lines \(\displaystyle AD\) and \(\displaystyle BC\) is parallel to \(\displaystyle AB\).

(5 pont)

Deadline expired on December 10, 2015.

Statistics:

157 students sent a solution.
5 points:	94 students.
4 points:	14 students.
3 points:	15 students.
2 points:	19 students.
1 point:	6 students.
0 point:	8 students.
Unfair, not evaluated:	1 solutions.

Problems in Mathematics of KöMaL, November 2015