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 be an isosceles triangle (). An arbitrary point is chosen on the extension of the beyond point . Prove that the sum of the radius of the circle inscribed in the triangle and the radius of the circle tangent to the side and the extensions of the sides of the triangle does not depend on the choice of point .