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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 10 December 2015.


Statistics:

158 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 solution.
Unfair, not evaluated:1 solution.

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