MathDB
Circumcenter of AOC belongs to BD

Source:

February 12, 2011
geometrycircumcircle

Problem Statement

The quadrilateral ABCDABCD is inscribed in a circle with center OO. The diagonals ACAC and BDBD do not pass through OO. If the circumcentre of triangle AOCAOC lies on the line BDBD, prove that the circumcentre of triangle BODBOD lies on the line ACAC.