Problem A. 726. (May 2018)

A. 726. In triangle \(\displaystyle ABC\) with incenter \(\displaystyle I\), line \(\displaystyle AI\) intersects the circumcircle of \(\displaystyle ABC\) at \(\displaystyle S\ne A\). Let the reflection of \(\displaystyle I\) with respect to \(\displaystyle BC\) be \(\displaystyle J\), and suppose that line \(\displaystyle SJ\) intersects the circumcircle of \(\displaystyle ABC\) for the second time at point \(\displaystyle P\ne S\). Show that \(\displaystyle AI=PI\).

Proposed by: József Mészáros, Galanta, Slovakia

(5 pont)

Deadline expired on June 11, 2018.

Statistics:

6 students sent a solution.
5 points:	Gáspár Attila, Matolcsi Dávid, Schrettner Jakab, Shuborno Das, Szabó Kristóf.
4 points:	GHENGHEA DANIEL.

Problems in Mathematics of KöMaL, May 2018