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Circles and Radical Axis

Source: 2016 Taiwan TST Round 2

July 17, 2016
geometryTaiwanTaiwan TSTgeometry solvedradical axispower of a pointlinearity of power of a point

Problem Statement

Let OO be the circumcenter of triangle ABCABC, and ω\omega be the circumcircle of triangle BOCBOC. Line AOAO intersects with circle ω\omega again at the point GG. Let MM be the midpoint of side BCBC, and the perpendicular bisector of BCBC meets circle ω\omega at the points OO and NN. Prove that the midpoint of the segment ANAN lies on the radical axis of the circumcircle of triangle OMGOMG, and the circle whose diameter is AOAO.
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