MathDB
Angle chasing yet again

Source: RMO 2018 P5

October 28, 2018
geometrycyclic quadrilateralcircumcircle

Problem Statement

In a cyclic quadrilateral ABCDABCD with circumcenter OO, the diagonals ACAC and BDBD intersect at XX. Let the circumcircles of triangles AXDAXD and BXCBXC intersect at YY. Let the circumcircles of triangles AXBAXB and CXDCXD intersect at ZZ. If OO lies inside ABCDABCD and if the points O,X,Y,ZO,X,Y,Z are all distinct, prove that O,X,Y,ZO,X,Y,Z lie on a circle.
Back to ProblemsView on AoPS