Problem B. 4789. (April 2016)

B. 4789. The interior angle bisectors drawn from vertices \(\displaystyle A\) and \(\displaystyle B\) in a triangle \(\displaystyle ABC\) intersect the circumscribed circle again at the points \(\displaystyle G\) and \(\displaystyle H\), respectively. The points of tangency of the inscribed circle of triangle \(\displaystyle ABC\) on sides \(\displaystyle BC\) and \(\displaystyle AC\) are \(\displaystyle D\) and \(\displaystyle E\), respectively. Let \(\displaystyle K\) denote the circumcentre of triangle \(\displaystyle DCE\). Show that the points \(\displaystyle G\), \(\displaystyle H\) and \(\displaystyle K\) are collinear.

Proposed by Sz. Miklós, Herceghalom

(4 pont)

Deadline expired on May 10, 2016.

Statistics:

86 students sent a solution.
4 points:	82 students.
2 points:	1 student.
1 point:	2 students.
0 point:	1 student.

Problems in Mathematics of KöMaL, April 2016