Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
 Already signed up? New to KöMaL?

# 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