Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem A. 660. (January 2016)

A. 660. The circle $\displaystyle \omega$ is inscribed in the quadrilateral $\displaystyle ABCD$. The incenters of the triangles $\displaystyle ABC$ and $\displaystyle ACD$ are $\displaystyle I$ and $\displaystyle J$, respectively. Let $\displaystyle T$ and $\displaystyle U$ be those two points on the arcs of $\displaystyle \omega$, lying in the triangles $\displaystyle ABC$ and $\displaystyle ACD$, respectively, for which the circles $\displaystyle ATC$ and $\displaystyle AUC$ are tangent to $\displaystyle \omega$. Show that the line segments $\displaystyle AC$, $\displaystyle IU$ and $\displaystyle JT$ are concurrent.

(5 pont)

Deadline expired on February 10, 2016.

### Statistics:

 3 students sent a solution. 5 points: Williams Kada. 2 points: 1 student. 0 point: 1 student.

Problems in Mathematics of KöMaL, January 2016