Problem B. 4765. (January 2016)

B. 4765. In a cyclic quadrilateral \(\displaystyle ABCD\), the angle bisectors of angles \(\displaystyle ADB\sphericalangle\) and \(\displaystyle ACB\sphericalangle\) intersect side \(\displaystyle AB\) at points \(\displaystyle E\) and \(\displaystyle F\), and the bisectors of \(\displaystyle CBD\sphericalangle\) and \(\displaystyle CAD\sphericalangle\) intersect side \(\displaystyle CD\) at \(\displaystyle G\) and \(\displaystyle H\), respectively. Prove that the points \(\displaystyle E\), \(\displaystyle F\), \(\displaystyle G\), \(\displaystyle H\) are concyclic.

Proposed by B. Bíró, Eger

(6 pont)

Deadline expired on February 10, 2016.

Statistics:

28 students sent a solution.
6 points:	Baran Zsuzsanna, Bodolai Előd, Cseh Kristóf, Csorba Benjámin, Czirkos Angéla, Gáspár Attila, Glasznova Maja, György Levente, Horváth András János, Imolay András, Kerekes Anna, Kovács 246 Benedek, Lakatos Ádám, Németh 123 Balázs, Pap Tibor, Schrettner Bálint, Stein Ármin, Tibay Álmos, Török Tímea, Váli Benedek, Wiandt Péter.
5 points:	Bukva Balázs.
3 points:	3 students.
2 points:	1 student.
0 point:	2 students.

Problems in Mathematics of KöMaL, January 2016