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Functional Equation related to incenter

Source: 2019 Korea Winter Program Practice Test 1 Problem 1

January 12, 2019
algebrafunctional equationfunctiongeometryincenter

Problem Statement

Find all functions f:R+ā†’R+f:\mathbb{R}^+\rightarrow\mathbb{R}^+ such that if a,b,ca,b,c are the length sides of a triangle, and rr is the radius of its incircle, then f(a),f(b),f(c)f(a),f(b),f(c) also form a triangle where its radius of the incircle is f(r)f(r).
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