Problem A. 705. (October 2017)

A. 705. Triangle \(\displaystyle ABC\) has orthocenter \(\displaystyle H\). Let \(\displaystyle D\) be a point distinct from the vertices on the circumcircle of \(\displaystyle ABC\). Suppose that circle \(\displaystyle BHD\) meets \(\displaystyle AB\) at \(\displaystyle P\ne B\), and circle \(\displaystyle CHD\) meets \(\displaystyle AC\) at \(\displaystyle Q\ne C\). Prove that as \(\displaystyle D\) moves on the circumcircle, the reflection of \(\displaystyle D\) across line \(\displaystyle PQ\) also moves on a fixed circle.

Proposed by Michael Ren, Andover, Massachusetts, USA

(5 pont)

Deadline expired on November 10, 2017.

Statistics:

16 students sent a solution.
5 points:	Beke Csongor, Bukva Balázs, Egri Máté, Gáspár Attila, Győrffy Ágoston, Imolay András, Márton Dénes, Matolcsi Dávid, Németh 123 Balázs, Schrettner Jakab, Szabó 417 Dávid, Szabó Kristóf.
1 point:	2 students.
0 point:	2 students.

Problems in Mathematics of KöMaL, October 2017