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sum of inradius + radius of mixtiinear excircle is fixed, start with isosceles

Source: 2006 All-Ukrainian Correspondence MO of magazine ''In the World of Mathematics'', grades 5-11 p10

April 28, 2021
geometrymixtilinear excircleradiiifixedisoscelesUkraine Correspondence

Problem Statement

Let ABCABC be an isosceles triangle (AB=ACAB=AC). An arbitrary point MM is chosen on the extension of the BCBC beyond point BB. Prove that the sum of the radius of the circle inscribed in the triangle AM​​BAM​​B and the radius of the circle tangent to the side ACAC and the extensions of the sides AM,CMAM, CM of the triangle AMCAMC does not depend on the choice of point MM.