Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem A. 632. (January 2015)

A. 632. Let \(\displaystyle ABCD\) be a convex quadrilateral. In the triangle \(\displaystyle ABC\) let \(\displaystyle I\) and \(\displaystyle J\) be the incenter and the excenter opposite to vertex \(\displaystyle A\), respectively. In the triangle \(\displaystyle ACD\) let \(\displaystyle K\) and \(\displaystyle L\) be the incenter and the excenter opposite to vertex \(\displaystyle A\), respectively. Show that the lines \(\displaystyle IL\) and \(\displaystyle JK\), and the bisector of the angle \(\displaystyle BCD\) are concurrent.

Russian problem

(5 pont)

Deadline expired on February 10, 2015.


Statistics:

5 students sent a solution.
5 points:Fehér Zsombor, Janzer Barnabás, Nagy-György Pál, Saranesh Prembabu, Williams Kada.

Problems in Mathematics of KöMaL, January 2015