Problem B. 4755. (December 2015)

B. 4755. In a triangle \(\displaystyle ABC\), the escribed circles \(\displaystyle k_A\) and \(\displaystyle k_B\) drawn to sides \(\displaystyle CB\) and \(\displaystyle CA\) touch the appropriate sides at \(\displaystyle D\) and \(\displaystyle E\), respectively. Show that line \(\displaystyle DE\) cuts out equal chords from the circles \(\displaystyle k_A\) and \(\displaystyle k_B\).

Proposed by K. Williams, Szeged

(4 pont)

Deadline expired on January 11, 2016.

Statistics:

94 students sent a solution.
4 points:	83 students.
3 points:	7 students.
2 points:	1 student.
1 point:	2 students.
0 point:	1 student.

Problems in Mathematics of KöMaL, December 2015