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Oral Sharygin Olympiad 2018 #6

Source: Problem 6; 10-11

April 18, 2018
Sharygin Geometry Olympiadgeometrycircumcircle

Problem Statement

Let ABCABC be an acute-angled triangle with circumcenter OO. The circumcircle of △BOC\triangle{BOC} meets the lines AB,ACAB, AC at points A1,A2A_1, A_2, respectively. Let ωA\omega_{A} be the circumcircle of triangle AA1A2AA_1A_2. Define ωB\omega_B and ωC\omega_C analogously. Prove that the circles ωA,ωB,ωC\omega_A, \omega_B, \omega_C concur on ⊙(ABC)\odot(ABC).
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