Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem B. 4684. (January 2015)

B. 4684. The diagonals of a quadrilateral $\displaystyle ABCD$ are perpendicular, they intersect at $\displaystyle E$. From point $\displaystyle E$, drop a perpendicular onto the line of each side. Consider the intersection of each perpendicular with the opposite side. Prove that the four points all lie on a circle centred at a point of the line segment connecting the midpoints of the diagonals.

Suggested by Sz. Miklós, Herceghalom

(5 pont)

Deadline expired on February 10, 2015.

### Statistics:

 34 students sent a solution. 5 points: Andó Angelika, Cseh Kristóf, Csépai András, Döbröntei Dávid Bence, Fekete Panna, Kovács 972 Márton, Molnár-Sáska Zoltán, Nagy-György Pál, Schrettner Bálint, Schwarcz Tamás, Szebellédi Márton, Varga-Umbrich Eszter, Williams Kada. 4 points: Bereczki Zoltán, Dömsödi Bálint, Gáspár Attila, Kocsis Júlia, Lajkó Kálmán, Mócsy Miklós, Nagy Kartal, Nagy-György Zoltán, Sal Kristóf, Stein Ármin, Török Zsombor Áron, Wiandt Péter. 3 points: 4 students. 2 points: 1 student. 1 point: 2 students. 0 point: 2 students.

Problems in Mathematics of KöMaL, January 2015