Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
 Already signed up? New to KöMaL?

# 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