MathDB
circumcenter of projections of P on sides of convex ABCD lies on MN, midpoints

Source: 2009 Balkan Shortlist BMO G3 - difficult

April 5, 2020
diagonalsprojectionsgeometrymidpointsconvex quadrilateralCircumcenterIsogonal conjugate

Problem Statement

Let ABCDABCD be a convex quadrilateral, and PP be a point in its interior. The projections of PP on the sides of the quadrilateral lie on a circle with center OO. Show that OO lies on the line through the midpoints of ACAC and BDBD.
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