Mathematical and Physical Journal
for High Schools
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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.


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