/sci/ - Science & Math

>>11048084

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