MathDB
Angle bisectors on cyclic quadrilateral

Source: Kosovo TST 2020 Problem 3

February 8, 2020
geometryangle bisectorcyclic quadrilateralharmonic range

Problem Statement

Let ABCDABCD be a cyclic quadrilateral with center OO such that BDBD bisects AC.AC. Suppose that the angle bisector of ABC\angle ABC intersects the angle bisector of ADC\angle ADC at a single point XX different than BB and D.D. Prove that the line passing through the circumcenters of triangles XACXAC and XBDXBD bisects the segment OX.OX.
Proposed by Viktor Ahmeti and Leart Ajvazaj, Kosovo