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