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# Nice Isongonal Conjugate

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.

Note by Alan Yan
1 year, 9 months ago