Problem

Source: 2009 Sharygin Geometry Olympiad Final Round problem 2 grade 8

Tags: geometry, cyclic quadrilateral, circumradius



A cyclic quadrilateral is divided into four quadrilaterals by two lines passing through its inner point. Three of these quadrilaterals are cyclic with equal circumradii. Prove that the fourth part also is cyclic quadrilateral and its circumradius is the same. (A.Blinkov)