MathDB

5

Part of 2005 IberoAmerican

Problems(1)

Prove that a line passes through the orthocenter

Source: Iberoamerican Olympiad 2005

9/29/2005
Let OO be the circumcenter of acutangle triangle ABCABC and let A1A_1 be some point in the smallest arc BCBC of the circumcircle of ABCABC. Let A2A_2 and A3A_3 points on sides ABAB and ACAC, respectively, such that ∠BA1A2=∠OAC\angle BA_1A_2 = \angle OAC and ∠CA1A3=∠OAB\angle CA_1A_3 = \angle OAB. Prove that the line A2A3A_2A_3 passes through the orthocenter of ABCABC.
geometrycircumcircletrigonometrygeometry solved