 Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# 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