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.


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

Problems in Mathematics of KöMaL, January 2016