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construct line that divides a triangle into 2 polygons of equal circumradii

Source: 2006 Oral Moscow Geometry Olympiad grades 10-11 p1

October 20, 2020
equal circlesconstructiongeometryCyclic

Problem Statement

An arbitrary triangle ABCABC is given. Construct a line that divides it into two polygons, which have equal radii of the circumscribed circles.
(L. Blinkov)