MathDB
Segment equal

Source: Chinese TST 2007 5th quiz P1

January 4, 2009
geometrycircumcircleparallelogramperpendicular bisectorgeometry proposed

Problem Statement

Let convex quadrilateral ABCD ABCD be inscribed in a circle centers at O. O. The opposite sides BA,CD BA,CD meet at H H, the diagonals AC,BD AC,BD meet at G. G. Let O1,O2 O_{1},O_{2} be the circumcenters of triangles AGD,BGC. AGD,BGC. O1O2 O_{1}O_{2} intersects OG OG at N. N. The line HG HG cuts the circumcircles of triangles AGD,BGC AGD,BGC at P,Q P,Q, respectively. Denote by M M the midpoint of PQ. PQ. Prove that NO \equal{} NM.
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