Let A B C be a scalene triangle with the longest side A C. (A scalene triangle has sides of different lengths.) Let P and Q be the points on the side A C such that A P=A B and C Q=C B. Thus we have a new triangle B P Q inside triangle A B C. Let k_{1} be the circle circumscribed around the triangle B P Q (that is, the circle passing through the vertices B, P, and Q of the triangle B P Q ); and let k_{2} be the circle inscribed in triangle A B C (that is, the circle inside triangle A B C that is tangent to the three sides A B, B C, and C A). Prove that the two circles k_{1} and k_{2} are concentric, that is, they have the same center.