Problem

Source: ELMO Shortlist 2024 G2

Tags: geometry, ELMO Shortlist



Let ABC be a triangle. Suppose that D, E, and F are points on segments ¯BC, ¯CA, and ¯AB respectively such that triangles AEF, BFD, and CDE have equal inradii. Prove that the sum of the inradii of AEF and DEF is equal to the inradius of ABC. Aprameya Tripathy