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Geometry Mathley 5.1 fixed line

Source:

June 7, 2020
midpointfixedfixed linecirclegeometry

Problem Statement

Let a,ba, b be two lines intersecting each other at OO. Point MM is not on either aa or bb. A variable circle (C)(C) passes through O,MO,M intersecting a,ba, b at A,BA,B respectively, distinct from OO. Prove that the midpoint of ABAB is on a fixed line.
Hạ Vũ Anh
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