MathDB
French pre-TST-2004/2005 #5

Source: Me

December 20, 2004
geometryincenterperimetertrigonometry

Problem Statement

Let II be the incenter of the triangle ABCABC. Let A1,A2A_1,A_2 be two distinct points on the line BCBC, let B1,B2B_1,B_2 be two distinct points on the line CACA, and let C1,C2C_1,C_2 be two distinct points on the line BABA such that AI=A1I=A2IAI = A_1I = A_2I and BI=B1I=B2IBI = B_1I = B_2I and CI=C1I=C2ICI = C_1I = C_2I. Prove that A1A2+B1B2+C1C2=pA_1A_2+B_1B_2+C_1C_2 = p where pp denotes the perimeter of ABC.ABC. Pierre.
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