MathDB
there is a circle with center O tangent to all 4 circumcircles , bicentric

Source: Mathley 2014.3 p6

August 19, 2020
geometrycircumcirclebicentric quadrilateraltangent circles

Problem Statement

A quadrilateral is called bicentric if it has both an incircle and a circumcircle. ABCDABCD is a bicentric quadrilateral with (O)(O) being its circumcircle. Let E,FE, F be the intersections of ABAB and CD,ADCD, AD and BCBC respectively. Prove that there is a circle with center OO tangent to all of the circumcircles of the four triangles EAD,EBC,FAB,FCDEAD, EBC, FAB, FCD.
Nguyen Van Linh, a student of the Vietnamese College, Ha Noi