Problem A. 368. (March 2005)
A. 368. The interior bisector of the angle A of the triangle ABC cuts the incircle c at two points; the one closer to A is denoted by O_{A}. Define the points O_{B} and O_{C} similarly on the internal bisectors of the angles B and C, respectively. The circle c_{A} is drawn about O_{A} and it is touching the sides AB and CA. Similarly, c_{B} is about O_{B} and it is touching the sides BC and AB, finally the circle c_{C} is about O_{C} and it is touching the sides CA and BC. Taken any two of the circles c_{A}, c_{B} and c_{C} consider their common external tangents different from the corresponding sides of the triangle, respectively. Prove that these three tangents are concurrent.
(5 pont)
Deadline expired on 15 April 2005.
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