Problem A. 559. (March 2012)

A. 559. The incircle of triangle ABC is k. The circle k_A touches k and the segments AB and AC at at A', A_B and A_C respectively. The circles k_B, k_C and the points B', C' are defined analogously. The second intersection point of the circles A'B'A_B and A'C'A_C, other than A', is K. The line A'K meets k at R, other than A'. Prove that R lies on the radical axis of the circles k_B and k_C.

(Kolmogorov's Cup, 2011; a problem by F. Ivlev)

(5 pont)

Deadline expired on April 10, 2012.

Statistics:

2 students sent a solution.
5 points:	Mester Márton, Omer Cerrahoglu.

Problems in Mathematics of KöMaL, March 2012