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construct line passing through B so that inradii of 2 small triangles are equal

Source: 2006 Oral Moscow Geometry Olympiad grades 8-9 p4

October 17, 2020
geometryequal circlesinradiusconstruction

Problem Statement

An arbitrary triangle ABCABC is given. Construct a straight line passing through vertex BB and dividing it into two triangles, the radii of the inscribed circles of which are equal.
(M. Volchkevich)