Let O be the circumcenter of an acute triangle ABC and A1 a point of the minor arc BC of the circle ABC . Let A2 and A3 be points on sides AB and AC respectively such that ∠BA1A2=∠OAC and ∠CA1A3=∠OAB . Points B2,B3,C2 and C3 are similarly constructed, with B2 in BC,B3 in AB,C2 in AC and C3 in BC. Prove that lines A2A3,B2B3 and C2C3 are concurrent. geometrycircumcircleconcurrencyconcurrent