Problem A. 774. (March 2020)

A. 774. Let $\displaystyle O$ be the circumcenter of triangle $\displaystyle ABC$, and $\displaystyle D$ be an arbitrary point on the circumcircle of $\displaystyle ABC$. Let points $\displaystyle X$, $\displaystyle Y$ and $\displaystyle Z$ be the orthogonal projections of point $\displaystyle D$ onto lines $\displaystyle OA$, $\displaystyle OB$ and $\displaystyle OC$, respectively. Prove that the incenter of triangle $\displaystyle XYZ$ is on the Simson-Wallace line of triangle $\displaystyle ABC$ corresponding to point $\displaystyle D$.

Submitted by Lajos Fonyó, Keszthely

(7 pont)

Deadline expired on April 14, 2020.

Statistics:

8 students sent a solution.
7 points:	Amaan Khan, Beke Csongor, Hegedűs Dániel, Várkonyi Zsombor, Weisz Máté.
6 points:	Bán-Szabó Áron, Seres-Szabó Márton.
1 point:	1 student.

Problems in Mathematics of KöMaL, March 2020