Mathematical and Physical Journal
for High Schools
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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.


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