Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem C. 1351. (April 2016)

C. 1351. Trapezium $\displaystyle ABCD$ has an inscribed circle that touches the sides $\displaystyle AB$, $\displaystyle BC$, $\displaystyle CD$ and $\displaystyle DA$ at points $\displaystyle E$, $\displaystyle F$, $\displaystyle G$ and $\displaystyle H$, respectively. The interior angle at vertex $\displaystyle B$ is $\displaystyle 60^\circ$. Let $\displaystyle I$ denote the intersection of lines $\displaystyle AD$ and $\displaystyle FG$, and let $\displaystyle K$ denote the midpoint of $\displaystyle FH$. Prove that if $\displaystyle HE$ is parallel to $\displaystyle BC$ then $\displaystyle IK$ is also parallel to them.

(5 pont)

Deadline expired on May 10, 2016.

### Statistics:

 74 students sent a solution. 5 points: 59 students. 4 points: 10 students. 3 points: 2 students. 2 points: 1 student. 1 point: 1 student. 0 point: 1 student.

Problems in Mathematics of KöMaL, April 2016