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Problem 593: Triangle, Circumcircle, Collinear Points. Level: Mathematics Education, High School, College

The figure shows a triangle ABC with the circumcircle O. D is any point and E is a point on the circumcircle O. Lines AD, BD, and CD meet the circumcircle O at A', B', and C', respectively. Lines EA', EB', and EC' meet lines BC, AC, and AB at A", B", and C", respectively. Prove that points A", B", C", and D are collinear.

Triangle, Circumcicle, Collinear Points

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