今年奥数几何题
设ABC是一个正三角形，点A,BC在三角形ABC的内部且满足\(BA_{1}=A_{1}C,CB_{1}=B{1}A,AC_{1}=C_{1}B\),及\(∠BA_{1}C+∠CB_{1}A+∠AC_{1}B=480\)度，
设直线\(BC_{1}\)与\(B_{1}C\)交于点\(A_{2}\),直线\(C_{1}A\)与\(A_{1}C\)交于点\(B_{2}\),直线\(A_{1}B\)与\(B_{1}A\)交于点\(C_{2}\)。
证明:若三角形\(A_{1}B_{1}C_{1}\)的三边长度两两不等,则三角形\(AA_{1}A_{2}\)、\(BB_{1}B_{2}\)和\(CC_{1}C_{2}\)的外接圆都经过两个公共点.
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