Geometry · Orthocentre · Circumcentre · Reflection of the orthocentre · Anticomplementary triangle · Midline
Let \(H\) be the orthocentre of an acute triangle \(ABC\), and let \(A_1\), \(B_1\) and \(C_1\) be the centres of the circles circumscribed about the triangles \(BHC\), \(CHA\) and \(AHB\) respectively. Prove that the triangles \(ABC\) and \(A_1B_1C_1\) are congruent.
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Serbian Regional Competition (Okruzno takmicenje) 2004, high school grade I, category A, problem 2. Organized by the Mathematical Society of Serbia (DMS). Source