Problem

Source: Israel TST 2 2025 p3

Tags: geometry, cyclic quadrilateral, circumcircle, angle bisector



Let ABCD be a cyclic quadrilateral with circumcenter O. The internal angle bisectors of DAB, ABC, BCD, CDA create a convex quadrilateral Q1. The external bisectors of the same angles create another convex quadrilateral Q2. Prove Q1, Q2 are cyclic, and that O is the midpoint of their circumcenters.