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 10 February 2015.
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