incentre of ABC lies on segment PQ iff AB + AC = 3BC, mixtilinear related
Source: RMM Shortlist 2017 G2
July 4, 2019
geometryincentermixtilinear
Problem Statement
Let be a triangle. Consider the circle internally tangent to the sides and , and to the circumcircle of the triangle , let be the point of contact of the two circles. Similarly, consider the circle internally tangent to the sides and , and to the circumcircle of the triangle , let be the point of contact of the two circles. Show that the incentre of the triangle lies on the segment if and only if .proposed by Luis Eduardo Garcia Hernandez, Mexico