Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem B. 4664. (November 2014)

B. 4664. A rectangle $\displaystyle ABDE$ is drawn to side $\displaystyle AB$ of an acute triangle $\displaystyle ABC$ on the inside, such that point $\displaystyle C$ should lie on the side $\displaystyle DE$. The rectangles $\displaystyle BCFG$ and $\displaystyle CAHI$ are defined in a similar way. ($\displaystyle A$ lies on line segment $\displaystyle FG$, and $\displaystyle B$ lies on line segment $\displaystyle HI$.) The midpoints of sides $\displaystyle AB$, $\displaystyle BC$, and $\displaystyle CA$ are $\displaystyle J$, $\displaystyle K$, and $\displaystyle L$, respectively. Prove that the sum of the angles $\displaystyle GJH\sphericalangle$, $\displaystyle IKD\sphericalangle$ and $\displaystyle ELF\sphericalangle$ is $\displaystyle 180^{\circ}$.

Suggested by Sz. Miklós, Herceghalom

(4 pont)

Deadline expired on December 10, 2014.

### Statistics:

 167 students sent a solution. 4 points: 159 students. 3 points: 4 students. 2 points: 1 student. 1 point: 1 student. 0 point: 2 students.

Problems in Mathematics of KöMaL, November 2014