Given a nonisosceles, nonright triangle \(ABC,\) let \(O\) denote the center of its circumscribed circle, and let \(A_1, B_1,\) and \(C_1\) be the midpoints of sides \(BC, CA,\) and \(AB,\) respectively. Point \(A_2\) is located on the ray \(OA_1\) so that \(\triangle OAA_1\) is similar to \(\triangle OA_2A\). Points \(B_2\) and \(C_2\) on rays \(OB_1\) and \(OC_1,\) respectively, are defined similarly. Prove that lines \(AA_2, BB_2,\) and \(CC_2\) are concurrent, i.e. these three lines intersect at a point.