fixed point for angle bisector of gray and black sides, 2 equal wooden disks
Source: Tournament of Towns, Junior A-Level , Spring 2019 p3
May 9, 2020
geometryangle bisectorcirclesdisksfixedFixed pointColoring
Problem Statement
Two equal non-intersecting wooden disks, one gray and one black, are glued to a plane. A triangle with one gray side and one black side can be moved along the plane so that the disks remain outside the triangle, while the colored sides of the triangle are tangent to the disks of the same color (the tangency points are not the vertices). Prove that the line that contains the bisector of the angle between the gray and black sides always passes through some fixed point of the plane.(Egor Bakaev, Pavel Kozhevnikov, Vladimir Rastorguev) (Senior version[url=https://artofproblemsolving.com/community/c6h2102856p15209040] here)