concyclic, ext.angle bisectors of quad - All-Russian MO 2000 Regional (R4) 10.7
Source:
September 26, 2024
geometryangle bisectorConcyclic
Problem Statement
In a convex quadrilateral we draw the bisectors , , , of external angles , , , respectively. The intersection points of the lines and , and , and , and are designated by , , , . It is known that perpendiculars drawn from on , from om , from on intersect at one point. Prove that the quadrilateral is cyclic.